Evaluate The Expression 1 2 ( 8 ) X {\dfrac{1}2(8)^x} 2 1 ​ ( 8 ) X For X = 2 {x=2} X = 2 . Related Content Report

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Introduction

In mathematics, evaluating expressions is a crucial skill that helps us solve problems and understand complex concepts. In this article, we will focus on evaluating the expression 12(8)x{\dfrac{1}2(8)^x} for x=2{x=2}. This involves substituting the value of x{x} into the expression and simplifying it to obtain the final result.

Understanding the Expression

The given expression is 12(8)x{\dfrac{1}2(8)^x}. This expression involves a fraction, a power, and a variable x{x}. To evaluate this expression, we need to understand the properties of exponents and fractions.

Exponents are a shorthand way of writing repeated multiplication. For example, 23{2^3} means 2×2×2{2 \times 2 \times 2}. In the given expression, (8)x{(8)^x} means 8{8} multiplied by itself x{x} times.

Fractions are a way of representing part of a whole. In the given expression, 12{\dfrac{1}2} means one half.

Substituting the Value of x{x}

To evaluate the expression, we need to substitute the value of x{x} into the expression. In this case, x=2{x=2}. So, we substitute x=2{x=2} into the expression:

12(8)2{\dfrac{1}2(8)^2}

Simplifying the Expression

Now that we have substituted the value of x{x}, we need to simplify the expression. To do this, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

In this case, we have:

12(8)2{\dfrac{1}2(8)^2}

First, we evaluate the exponent:

(8)2=64{(8)^2 = 64}

So, the expression becomes:

12(64){\dfrac{1}2(64)}

Next, we multiply 12{\dfrac{1}2} by 64{64}:

12(64)=32{\dfrac{1}2(64) = 32}

Therefore, the final result is:

32{32}

Conclusion

In this article, we evaluated the expression 12(8)x{\dfrac{1}2(8)^x} for x=2{x=2}. We substituted the value of x{x} into the expression and simplified it using the order of operations. The final result is 32{32}. This problem demonstrates the importance of understanding exponents and fractions in mathematics.

Related Content

Discussion

  • What is the importance of evaluating expressions in mathematics?
  • How do you simplify expressions with exponents and fractions?
  • What are some common mistakes to avoid when evaluating expressions?

Further Reading

References

Note: The references and further reading sections are not included in the word count.

Introduction

In our previous article, we evaluated the expression 12(8)x{\dfrac{1}2(8)^x} for x=2{x=2}. We substituted the value of x{x} into the expression and simplified it using the order of operations. In this article, we will answer some frequently asked questions related to evaluating expressions with exponents and fractions.

Q&A

Q: What is the importance of evaluating expressions in mathematics?

A: Evaluating expressions is a crucial skill in mathematics that helps us solve problems and understand complex concepts. It involves substituting values into expressions and simplifying them to obtain the final result.

Q: How do you simplify expressions with exponents and fractions?

A: To simplify expressions with exponents and fractions, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What are some common mistakes to avoid when evaluating expressions?

A: Some common mistakes to avoid when evaluating expressions include:

  • Not following the order of operations
  • Not simplifying expressions correctly
  • Not checking for errors in calculations
  • Not using parentheses correctly

Q: How do you evaluate expressions with negative exponents?

A: To evaluate expressions with negative exponents, we need to use the rule that a−n=1an{a^{-n} = \dfrac{1}{a^n}}. For example, 2−3=123=18{2^{-3} = \dfrac{1}{2^3} = \dfrac{1}{8}}.

Q: How do you evaluate expressions with fractional exponents?

A: To evaluate expressions with fractional exponents, we need to use the rule that am/n=amn{a^{m/n} = \sqrt[n]{a^m}}. For example, 23/2=23=8=22{2^{3/2} = \sqrt{2^3} = \sqrt{8} = 2\sqrt{2}}.

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

A: An exponent is a small number that is raised to a power, while a power is the result of raising a number to an exponent. For example, in the expression 23{2^3}, the exponent is 3 and the power is 8.

Q: How do you evaluate expressions with multiple exponents?

A: To evaluate expressions with multiple exponents, we need to follow the order of operations and use the rule that am+n=am⋅an{a^{m+n} = a^m \cdot a^n}. For example, in the expression 23+2{2^{3+2}}, we need to evaluate the exponent first and then multiply the results.

Conclusion

In this article, we answered some frequently asked questions related to evaluating expressions with exponents and fractions. We covered topics such as the importance of evaluating expressions, simplifying expressions with exponents and fractions, and common mistakes to avoid. We also discussed how to evaluate expressions with negative exponents, fractional exponents, and multiple exponents.

Related Content

Discussion

  • What are some common mistakes to avoid when evaluating expressions?
  • How do you simplify expressions with exponents and fractions?
  • What are some real-world applications of evaluating expressions?

Further Reading

References