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Exponent Practice Problems

Exponent Practice Problems are a great way to build your understanding of exponent rules and improve your performance on the ACT Math test. These problems cover common exponent problems, including multiplying powers, raising a power to another power, zero and negative exponents, and simplifying expressions.

This set of exponent practice problems includes different types of exponent questions to help you recognize exponent rules and apply them correctly. You will also find more challenging hard exponent problems that require you to combine multiple rules and solve multi-step expressions.

Before working through the questions, review the fundamental laws of exponents. For a base x and exponents m and n, some of the most important rules are:

$$ x^m \cdot x^n=x^{m+n} \qquad\text{and}\qquad (x^m)^n=x^{mn}. $$

For example:

$$ x^3\cdot x^5=x^8 \qquad\text{and}\qquad (x^3)^5=x^{15}. $$

Understanding these rules will help you solve exponent math problems more accurately and efficiently. Continue with the practice questions below, then check the answers and solutions to identify any exponent rules that you need to review.

1. What is $(2x^3)^4$ equal to? 2

$ 8x^7 $
$ 4x^{12} $
$ 16x^{12} $
$2x^7 $

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C

2. Which of the following is equivalent to $\left(\!\!\dfrac{2a^4b^5}{3c^7}\!\right)^5$ if $c\!\ne\! 0$? 3

$\dfrac{32a^{20}b^{25}}{81c^{35}} $
$\dfrac{32a^{20}b^{25}}{243c^{25}}$
$\dfrac{32a^{20}b^{25}}{243c^{40}}$
$\dfrac{32a^{20}b^{25}}{243c^{35}}$

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D

3. Which of the following is equivalent to $\dfrac{\left(\!\dfrac{x^{11}}{x^3}\!\right)^2}{\dfrac{x^5}{x^2}}$ if $x\!\ne\! 0$? 2

$x^{10}$
$x^{16}$
$ x^5$
$ x^{13}$

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D

4. Which of the following is equivalent to $\left(\dfrac{4}{3}\right)^{\dfrac{-5}{2}}$? 4

$\dfrac{9\sqrt{3}}{4}$
$\dfrac{9\sqrt{3}}{32}$
$ \dfrac{9\sqrt{3}}{8} $
$\dfrac{9\sqrt{3}}{16}$

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B

5. Which of the following is equivalent to $(x^3)^5\cdot(x^4)^6$? 3

$x^{41}$
$x^{21}$
$x^{360}$
$x^{39}$

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D

6. Which of the following is equivalent to $(2a^{10}\sqrt{b})^4 $? 3

$64a^{40}b^2$
$16a^{40}b^2$
$16a^{20}b^2$
$8a^{40}b^2$

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B

Answer key: 1.C, 2.D, 3.D, 4.B, 5.D, 6.B.

Solutions

1. (C) $2^4 (x^3)^4=16 x^{12}$.

2. (D) $\dfrac{2^5{(a^4)}^5{(b^5)}^5}{3^5{(c^7)}^5}= \dfrac{32a^{20}b^{25}}{243c^{35}}$.

3. (D) $\dfrac{({x^8})^2}{x^3}=\dfrac{x^{16}}{x^3}=x^{13}$.

4. (B) $\dfrac{(\sqrt{3})^5}{(\sqrt{4})^5}= \dfrac{9\sqrt{3}}{2^5}=\dfrac{9\sqrt{3} }{32}$.

5. (D) $x^{15}\cdot x^{24}=x^{39} $.

6. (B) Take the constant to the power and multiply the exponents: $(2a^{10}\sqrt{b})^4 = 16a^{40}b^2$.

Difficulty Key

1 Easiest
2 – 4 Intermediate
5 Most Difficult

Why Exponent Practice Problems Matter on the ACT

Exponent practice problems are an important way to strengthen your algebra skills and prepare for ACT Math. These questions test your ability to simplify expressions and apply exponent rules correctly.

Some exponent problems may look complicated at first, but recognizing the correct rule can make them much easier to solve. Practicing different types of exponent questions can also help you improve accuracy and confidence with algebraic expressions.

Key Exponent Rules You Must Know

When solving exponent practice problems, make sure you understand these basic rules:

Multiply powers with the same base → add the exponents
Divide powers with the same base → subtract the exponents
Raise a power to another power → multiply the exponents
Negative exponents → use the reciprocal
Zero exponent → equals 1 for any nonzero base

Common Mistakes Students Make With Exponents

When working through exponent questions, students often make mistakes such as:

Applying an exponent rule when the bases are different
Confusing the multiplication rule with the power-of-a-power rule
Forgetting how to rewrite negative exponents
Incorrectly simplifying expressions with zero exponents
Not simplifying the final expression completely

ACT Exam Strategy for Exponent Problems

When you encounter exponent problems on the ACT, focus on identifying the rule you need before doing unnecessary calculations.

The best strategy is to:

Identify the exponent rule being used
Rewrite the expression when necessary
Simplify one step at a time
Avoid unnecessary calculations
Check your exponents before choosing an answer

How to Improve Your Exponent Practice

Regular practice with different types of exponent math problems can help you recognize common patterns more quickly. Start with basic exponent rules, then move on to more challenging problems that require multiple steps.

If you make a mistake, review the rule that applies to the problem rather than only checking the correct answer. This will help you solve similar exponents problems more accurately in the future.

Related ACT Math Practice

You can also strengthen your algebra skills by practicing scientific notation problems and linear equations in one variable .