Evaluate { (2 \times 5)^3$}$.
Introduction
In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In this article, we will evaluate the expression {(2 \times 5)^3$}$ using the order of operations.
Understanding the Expression
The given expression is {(2 \times 5)^3$}$. To evaluate this expression, we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses, which is ${2 \times 5\$}.
Evaluating the Expression Inside the Parentheses
To evaluate the expression ${2 \times 5\$}, we need to multiply 2 and 5. Multiplication is a basic arithmetic operation that involves finding the product of two numbers. In this case, the product of 2 and 5 is 10.
Evaluating the Expression Outside the Parentheses
Now that we have evaluated the expression inside the parentheses, we can substitute the result into the original expression. The original expression is {(2 \times 5)^3$}$, and we have found that ${2 \times 5 = 10\$}. Therefore, the expression becomes ${10^3\$}.
Evaluating the Exponent
The next step is to evaluate the exponent. In this case, the exponent is 3, and the base is 10. To evaluate the exponent, we need to multiply the base by itself 3 times. This can be written as ${10 \times 10 \times 10\$}.
Evaluating the Product
To evaluate the product ${10 \times 10 \times 10\$}, we need to multiply 10 by itself 3 times. This can be written as ${10^3\$}. To evaluate ${10^3\$}, we need to multiply 10 by itself 3 times.
Calculating the Final Result
To calculate the final result, we need to multiply 10 by itself 3 times. This can be written as ${10 \times 10 \times 10\$}. Multiplying 10 by itself 3 times gives us a result of 1000.
Conclusion
In conclusion, the expression {(2 \times 5)^3$}$ can be evaluated using the order of operations. The first step is to evaluate the expression inside the parentheses, which is ${2 \times 5\$}. The product of 2 and 5 is 10. The next step is to substitute the result into the original expression, which becomes ${10^3\$}. The exponent is 3, and the base is 10. To evaluate the exponent, we need to multiply the base by itself 3 times. This can be written as ${10 \times 10 \times 10\$}. Multiplying 10 by itself 3 times gives us a result of 1000.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, you need to evaluate the expression inside the parentheses first. This means that you need to perform any operations inside the parentheses before you can perform any operations outside the parentheses.
Q: How do I evaluate an exponent?
A: To evaluate an exponent, you need to multiply the base by itself as many times as the exponent indicates. For example, if the exponent is 3, you need to multiply the base by itself 3 times.
Q: What is the result of {(2 \times 5)^3$}$?
A: The result of {(2 \times 5)^3$}$ is 1000.
Final Answer
The final answer is:
Introduction
Evaluating mathematical expressions can be a challenging task, especially when there are multiple operations involved. In this article, we will provide answers to some frequently asked questions about evaluating mathematical expressions.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, you need to evaluate the expression inside the parentheses first. This means that you need to perform any operations inside the parentheses before you can perform any operations outside the parentheses.
Q: How do I evaluate an exponent?
A: To evaluate an exponent, you need to multiply the base by itself as many times as the exponent indicates. For example, if the exponent is 3, you need to multiply the base by itself 3 times.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve finding the product or quotient of two numbers. However, the key difference between the two is that multiplication involves finding the product of two numbers, while division involves finding the quotient of two numbers.
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. This means that you need to perform any operations inside parentheses first, followed by any exponents, and then any multiplication and division operations from left to right. Finally, you need to perform any addition and subtraction operations from left to right.
Q: What is the result of {(2 \times 5)^3$}$?
A: The result of {(2 \times 5)^3$}$ is 1000.
Q: How do I simplify an expression?
A: To simplify an expression, you need to combine like terms and eliminate any unnecessary operations. This can involve combining constants, combining variables, or eliminating any operations that are not necessary.
Q: What is the difference between a variable and a constant?
A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change. For example, x is a variable, while 5 is a constant.
Q: How do I evaluate an expression with variables?
A: To evaluate an expression with variables, you need to substitute the value of the variable into the expression. This can involve replacing the variable with a numerical value or another expression.
Q: What is the result of {x^2 + 5x + 3$}$?
A: The result of {x^2 + 5x + 3$}$ depends on the value of x. If x is a specific value, you can substitute that value into the expression and evaluate it. However, if x is a variable, the expression is an algebraic expression and cannot be evaluated without knowing the value of x.
Conclusion
Evaluating mathematical expressions can be a challenging task, especially when there are multiple operations involved. However, by following the order of operations and understanding the rules of arithmetic, you can evaluate even the most complex expressions. In this article, we have provided answers to some frequently asked questions about evaluating mathematical expressions.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, you need to evaluate the expression inside the parentheses first. This means that you need to perform any operations inside the parentheses before you can perform any operations outside the parentheses.
Q: How do I evaluate an exponent?
A: To evaluate an exponent, you need to multiply the base by itself as many times as the exponent indicates. For example, if the exponent is 3, you need to multiply the base by itself 3 times.
Q: What is the result of {(2 \times 5)^3$}$?
A: The result of {(2 \times 5)^3$}$ is 1000.
Final Answer
The final answer is: