What Is The Value Of The Expression ( 7.2 × 10 4 ) ÷ 400 \left(7.2 \times 10^4\right) \div 400 ( 7.2 × 1 0 4 ) ÷ 400 ?A. 180 × 10 2 180 \times 10^2 180 × 1 0 2 B. 1.8 × 10 2 1.8 \times 10^2 1.8 × 1 0 2 C. 1.8 × 10 1 1.8 \times 10^1 1.8 × 1 0 1 D. 0.18 × 10 2 0.18 \times 10^2 0.18 × 1 0 2

Mar 12, 2025 by ADMIN 289 views

$What is the Value of the Expression $\left(7.2 \times 10^4\right) \div 400$?$

Understanding the Expression

The given expression is $\left(7.2 \times 10^4\right) \div 400$ . To evaluate this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, we have a division operation inside the parentheses.

Evaluating the Expression

To evaluate the expression, we can start by dividing $7.2 \times 10^4$ by $400$ . However, before we do that, let's simplify the expression by converting the decimal number $7.2$ to a scientific notation. We can write $7.2$ as $7.2 \times 10^0$ .

Simplifying the Expression

Now, we can rewrite the expression as $\left(7.2 \times 10^0 \times 10^4\right) \div 400$ . Using the properties of exponents, we can simplify this expression by adding the exponents of $10$ . This gives us $\left(7.2 \times 10^4\right) \div 400 = \left(7.2 \times 10^4\right) \div \left(4 \times 10^2\right)$ .

Dividing Numbers in Scientific Notation

To divide numbers in scientific notation, we can divide the coefficients and subtract the exponents of $10$ . In this case, we have $\frac{7.2}{4} \times 10^{4-2}$ . Simplifying this expression, we get $1.8 \times 10^2$ .

Conclusion

Therefore, the value of the expression $\left(7.2 \times 10^4\right) \div 400$ is $1.8 \times 10^2$ .

Comparison with Answer Choices

Let's compare our answer with the answer choices given in the problem. We have:

A. $180 \times 10^2$
B. $1.8 \times 10^2$
C. $1.8 \times 10^1$
D. $0.18 \times 10^2$

Our answer, $1.8 \times 10^2$ , matches answer choice B.

Final Answer

The final answer is $\boxed{1.8 \times 10^2}$ .

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: How do we evaluate an expression with a division operation inside the parentheses?

A: We can start by simplifying the expression inside the parentheses and then evaluate the division operation.

Q: How do we divide numbers in scientific notation?

A: We can divide the coefficients and subtract the exponents of $10$ .

Q: What is the value of the expression $\left(7.2 \times 10^4\right) \div 400$ ?

A: The value of the expression $\left(7.2 \times 10^4\right) \div 400$ is $1.8 \times 10^2$ .

Step-by-Step Solution

Simplify the expression inside the parentheses by converting the decimal number $7.2$ to a scientific notation.
Rewrite the expression as $\left(7.2 \times 10^0 \times 10^4\right) \div 400$ .
Simplify the expression by adding the exponents of $10$ .
Divide the coefficients and subtract the exponents of $10$ .
Simplify the expression to get the final answer.

Common Mistakes

Failing to simplify the expression inside the parentheses.
Failing to add the exponents of $10$ .
Failing to divide the coefficients and subtract the exponents of $10$ .

Tips and Tricks

Make sure to follow the order of operations.
Simplify the expression inside the parentheses before evaluating the division operation.
Use the properties of exponents to simplify the expression.
Divide the coefficients and subtract the exponents of $10$ when dividing numbers in scientific notation.

Q: What is the order of operations?

A: The order of operations is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: How do I evaluate an expression with a division operation inside the parentheses?

A: To evaluate an expression with a division operation inside the parentheses, you need to simplify the expression inside the parentheses first and then evaluate the division operation.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to add or subtract the exponents of the same base.

Q: How do I divide numbers in scientific notation?

A: To divide numbers in scientific notation, you need to divide the coefficients and subtract the exponents of 10.

Q: What is the value of the expression $\left(7.2 \times 10^4\right) \div 400$ ?

A: The value of the expression $\left(7.2 \times 10^4\right) \div 400$ is $1.8 \times 10^2$ .

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, you need to follow the order of operations and evaluate the operations from left to right.

Q: What is the difference between a coefficient and an exponent?

A: A coefficient is a number that is multiplied by a variable or an expression, while an exponent is a power to which a number or variable is raised.

Q: How do I simplify an expression with a negative exponent?

A: To simplify an expression with a negative exponent, you need to rewrite the expression with a positive exponent by taking the reciprocal of the coefficient.

Q: What is the value of the expression $\left(2 \times 10^3\right) \div \left(5 \times 10^2\right)$ ?

A: The value of the expression $\left(2 \times 10^3\right) \div \left(5 \times 10^2\right)$ is $0.4 \times 10^1$ .

Q: How do I evaluate an expression with a variable in the exponent?

A: To evaluate an expression with a variable in the exponent, you need to use the properties of exponents to simplify the expression.

Q: What is the value of the expression $\left(3x^2\right) \div \left(2x^3\right)$ ?

A: The value of the expression $\left(3x^2\right) \div \left(2x^3\right)$ is $\frac{3}{2}x^{-1}$ .

Q: How do I simplify an expression with a fraction in the exponent?

A: To simplify an expression with a fraction in the exponent, you need to use the properties of exponents to simplify the expression.

Q: What is the value of the expression $\left(2^3\right)^4$ ?

A: The value of the expression $\left(2^3\right)^4$ is $2^{12}$ .

Q: How do I evaluate an expression with multiple exponents?

A: To evaluate an expression with multiple exponents, you need to use the properties of exponents to simplify the expression.

Q: What is the value of the expression $\left(2^3 \times 3^2\right)^4$ ?

A: The value of the expression $\left(2^3 \times 3^2\right)^4$ is $\left(2^3\right)^4 \times \left(3^2\right)^4 = 2^{12} \times 3^8$ .

Q: How do I simplify an expression with a negative exponent and a fraction?

A: To simplify an expression with a negative exponent and a fraction, you need to use the properties of exponents and fractions to simplify the expression.

Q: What is the value of the expression $\left(\frac{1}{2}\right)^{-3}$ ?

A: The value of the expression $\left(\frac{1}{2}\right)^{-3}$ is $2^3 = 8$ .

Q: How do I evaluate an expression with a variable in the exponent and a fraction?

A: To evaluate an expression with a variable in the exponent and a fraction, you need to use the properties of exponents and fractions to simplify the expression.

Q: What is the value of the expression $\left(\frac{1}{x}\right)^{-2}$ ?

A: The value of the expression $\left(\frac{1}{x}\right)^{-2}$ is $x^2$ .

Q: How do I simplify an expression with multiple exponents and fractions?

A: To simplify an expression with multiple exponents and fractions, you need to use the properties of exponents and fractions to simplify the expression.

Q: What is the value of the expression $\left(\frac{2}{3}\right)^{-2} \times \left(\frac{3}{4}\right)^{-1}$ ?

A: The value of the expression $\left(\frac{2}{3}\right)^{-2} \times \left(\frac{3}{4}\right)^{-1}$ is $\frac{9}{4} \times 4 = 9$ .

Q: How do I evaluate an expression with a variable in the exponent and multiple fractions?

A: To evaluate an expression with a variable in the exponent and multiple fractions, you need to use the properties of exponents and fractions to simplify the expression.

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1}$ ?

A: The value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1}$ is $x^2 \times y = xy^2$ .

Q: How do I simplify an expression with multiple exponents and variables?

A: To simplify an expression with multiple exponents and variables, you need to use the properties of exponents and variables to simplify the expression.

Q: What is the value of the expression $\left(x^2 \times y^3\right)^4$ ?

A: The value of the expression $\left(x^2 \times y^3\right)^4$ is $\left(x^2\right)^4 \times \left(y^3\right)^4 = x^8 \times y^{12}$ .

Q: How do I evaluate an expression with multiple exponents and variables with fractions?

A: To evaluate an expression with multiple exponents and variables with fractions, you need to use the properties of exponents, variables, and fractions to simplify the expression.

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4$ ?

A: The value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4$ is $x^2 \times y^2 \times x^8 \times y^{12} = x^{10} \times y^{14}$ .

Q: How do I simplify an expression with multiple exponents, variables, and fractions?

A: To simplify an expression with multiple exponents, variables, and fractions, you need to use the properties of exponents, variables, and fractions to simplify the expression.

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2}$ ?

A: The value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2}$ is $x^{10} \times y^{14} \times 9 = 9x^{10} \times y^{14}$ .

Q: How do I evaluate an expression with multiple exponents, variables, fractions, and decimals?

A: To evaluate an expression with multiple exponents, variables, fractions, and decimals, you need to use the properties of exponents, variables, fractions, and decimals to simplify the expression.

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2} \times 0.5$ ?

A: The value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)4 \times \left(\frac{2}{3}\right)^{-2} \times

Understanding the Expression

Evaluating the Expression

Simplifying the Expression

Dividing Numbers in Scientific Notation

Conclusion

Comparison with Answer Choices

Final Answer

Frequently Asked Questions

Q: What is the order of operations?

Q: How do we evaluate an expression with a division operation inside the parentheses?

Q: How do we divide numbers in scientific notation?

Q: What is the value of the expression (7.2×104)÷400\left(7.2 \times 10^4\right) \div 400(7.2×104)÷400?

Step-by-Step Solution

Common Mistakes

Tips and Tricks

Q: What is the order of operations?

Q: How do I evaluate an expression with a division operation inside the parentheses?

Q: How do I simplify an expression with exponents?

Q: How do I divide numbers in scientific notation?

Q: What is the value of the expression (7.2×104)÷400\left(7.2 \times 10^4\right) \div 400(7.2×104)÷400?

Q: How do I evaluate an expression with multiple operations?

Q: What is the difference between a coefficient and an exponent?

Q: How do I simplify an expression with a negative exponent?

Q: What is the value of the expression (2×103)÷(5×102)\left(2 \times 10^3\right) \div \left(5 \times 10^2\right)(2×103)÷(5×102)?

Q: How do I evaluate an expression with a variable in the exponent?

Q: What is the value of the expression (3x2)÷(2x3)\left(3x^2\right) \div \left(2x^3\right)(3x2)÷(2x3)?

Q: How do I simplify an expression with a fraction in the exponent?

Q: What is the value of the expression (23)4\left(2^3\right)^4(23)4?

Q: How do I evaluate an expression with multiple exponents?

Q: What is the value of the expression (23×32)4\left(2^3 \times 3^2\right)^4(23×32)4?

Q: How do I simplify an expression with a negative exponent and a fraction?

Q: What is the value of the expression (12)−3\left(\frac{1}{2}\right)^{-3}(21​)−3?

Q: How do I evaluate an expression with a variable in the exponent and a fraction?

Q: What is the value of the expression (1x)−2\left(\frac{1}{x}\right)^{-2}(x1​)−2?

Q: How do I simplify an expression with multiple exponents and fractions?

Q: What is the value of the expression (23)−2×(34)−1\left(\frac{2}{3}\right)^{-2} \times \left(\frac{3}{4}\right)^{-1}(32​)−2×(43​)−1?

Q: How do I evaluate an expression with a variable in the exponent and multiple fractions?

Q: What is the value of the expression (xy)−2×(yx)−1\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1}(yx​)−2×(xy​)−1?

Q: How do I simplify an expression with multiple exponents and variables?

Q: What is the value of the expression (x2×y3)4\left(x^2 \times y^3\right)^4(x2×y3)4?

Q: How do I evaluate an expression with multiple exponents and variables with fractions?

Q: What is the value of the expression (xy)−2×(yx)−1×(x2×y3)4\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4(yx​)−2×(xy​)−1×(x2×y3)4?

Q: How do I simplify an expression with multiple exponents, variables, and fractions?

Q: What is the value of the expression (xy)−2×(yx)−1×(x2×y3)4×(23)−2\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2}(yx​)−2×(xy​)−1×(x2×y3)4×(32​)−2?

Q: How do I evaluate an expression with multiple exponents, variables, fractions, and decimals?

Q: What is the value of the expression (xy)−2×(yx)−1×(x2×y3)4×(23)−2×0.5\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2} \times 0.5(yx​)−2×(xy​)−1×(x2×y3)4×(32​)−2×0.5?

Q: What is the value of the expression $\left(7.2 \times 10^4\right) \div 400$ ?

Q: What is the value of the expression $\left(7.2 \times 10^4\right) \div 400$ ?

Q: What is the value of the expression $\left(2 \times 10^3\right) \div \left(5 \times 10^2\right)$ ?

Q: What is the value of the expression $\left(3x^2\right) \div \left(2x^3\right)$ ?

Q: What is the value of the expression $\left(2^3\right)^4$ ?

Q: What is the value of the expression $\left(2^3 \times 3^2\right)^4$ ?

Q: What is the value of the expression $\left(\frac{1}{2}\right)^{-3}$ ?

Q: What is the value of the expression $\left(\frac{1}{x}\right)^{-2}$ ?

Q: What is the value of the expression $\left(\frac{2}{3}\right)^{-2} \times \left(\frac{3}{4}\right)^{-1}$ ?

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1}$ ?

Q: What is the value of the expression $\left(x^2 \times y^3\right)^4$ ?

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4$ ?

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2}$ ?

Q: What is the value of the expression $\left(\frac{x}{y}\right)^{-2} \times \left(\frac{y}{x}\right)^{-1} \times \left(x^2 \times y^3\right)^4 \times \left(\frac{2}{3}\right)^{-2} \times 0.5$ ?