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High School Math : How to evaluate exponents

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Example Questions

Example Question #11 : How To Evaluate Exponents

Simplify:

$(x^{3})^{8}$

Possible Answers:

$x^{5}$

$x^{24}$

$x^{27}$

$x^{11}$

Correct answer:

$x^{24}$

Explanation:

When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.

So we multiply by to get the power of the answer, .

The answer is $x^{24}$ .

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Example Question #11 : How To Use The Power Rule For Exponents In Pre Algebra

Which of the following is equivalent to:

$(2^{6})^{\frac{2}{3}}$ ?

Possible Answers:

26.3

Correct answer:

Explanation:

Recall that when we have the exponent of an expression with an exponent, as in this case, we multiply these exponents. Thus, we have that:

$(2^{6})^{\frac{2}{3}} = 2^{6\cdot \frac{2}{3}} = 2^{\frac{12}{3}} = 2^{4} = 16$

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Example Question #12 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify $(x^{5})^{9}$

Possible Answers:

x^5

$x^{45}$

$x^{14}$

x^9

Correct answer:

$x^{45}$

Explanation:

When raising a power to a power, multiply the power inside the parentheses by the power outside the parentheses. In this case, multiply by to find the power of the answer, .

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Example Question #13 : How To Use The Power Rule For Exponents In Pre Algebra

Which of the following is equivalent to (X^2)^5 ?

Possible Answers:

$X^{7}$

$X^{10}$

$X^{5}$

$X^{25}$

$X^{3}$

Correct answer:

$X^{10}$

Explanation:

When an exponent expression is raised by another exponent, you can multiply the exponents:

$(X^{2})^{5}=X^{2 \cdot 5}=X^{10}$

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Example Question #14 : How To Use The Power Rule For Exponents In Pre Algebra

Simplify:

$5^{-2}$

Possible Answers:

$\frac{1}{25}$

$\frac{1}{10}$

$-\frac{1}{10}$

$-\frac{1}{25}$

Correct answer:

$\frac{1}{25}$

Explanation:

To get rid of the negative exponent, find the inverse of $5^{-2}$ , which is $\frac{1}{5^{2}}$ .

$5 \times 5 =25$ , so the final answer is $\frac{1}{25}$ .

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Example Question #15 : How To Use The Power Rule For Exponents In Pre Algebra

$(x^{5})^3=$

Possible Answers:

x^8

$x^{15}$

$x^{75}$

$x^{25}$

x^2

Correct answer:

$x^{15}$

Explanation:

According to the power rule of exponents, you multiply the exponents when you raise a power to a power.

$(x^5)^3=x^{5 * 3}=x^{15}$

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Example Question #16 : How To Use The Power Rule For Exponents In Pre Algebra

(3^2)^4=?

Possible Answers:

1296

729

6561

Correct answer:

6561

Explanation:

According to the power rule for exponents, we can simplify (3^2)^4=3^8 and

3^8=6561

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Example Question #11 : How To Evaluate Exponents

Simplify the following expression.

$2^{3}*2^{5}$

Possible Answers:

$4^{15}$

$4^{8}$

$2^{2}$

$2^{15}$

$2^{8}$

Correct answer:

$2^{8}$

Explanation:

$2^{3}*2^{5}$

This expression is a product of exponents with like bases. In these situations, we should use the product rule, which states that we should add the exponents.

$2^3*2^5=2^{3+5}=2^8$

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Example Question #12 : How To Evaluate Exponents

Simplify $2^{4}2^{12}$ without evaluating.

Possible Answers:

Cannot be simplified

$2^{8}$

$2^{16}$

$2^{14}$

$2^{24}$

Correct answer:

$2^{16}$

Explanation:

When multilping 2 numbers with exponents, if the bases are the same, they can be combined and the exponents add together.

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Example Question #915 : High School Math

Evaluate $\dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}$

Possible Answers:

$\dpi{100} x^{x^{2}-x+7}$

$x^{2x^{2}-5x+13}$

$\dpi{100} x^{x^{2}-2x+6}$

$\dpi{100} x^{4x^{2}-10x+26}$

$x^{4x-7}$

Correct answer:

$x^{2x^{2}-5x+13}$

Explanation:

The quotient rule for exponents states that when like numbers are raised to a certain power, then their exponents are subtracted from one another.

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{(4x^{2}-3x+7)-(2x^{2}+2x-6)}$

Solve for the exponent equation.

$(4x^{2}-3x+7)-(2x^{2}+2x-6)=4x^{2}-3x+7-2x^{2}-2x+6$

Combine like terms.

$\rightarrow (2x^{2}-5x+13)$

Therefore,

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{2x^{2}-5x+13}$

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High School Math : How to evaluate exponents

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : How To Evaluate Exponents

Example Question #11 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #12 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #13 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #14 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #15 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #16 : How To Use The Power Rule For Exponents In Pre Algebra

Example Question #11 : How To Evaluate Exponents

Example Question #12 : How To Evaluate Exponents

Example Question #915 : High School Math

All High School Math Resources

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