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SAT Exponents: Lesson, Practice Problems & Video Explanations

By Glyn Caddell, BSME · Author of Digital SAT Math Secrets · Tutoring since 2008 — Updated August 18, 2026

Digital SAT Exponents

Exponents questions on the SAT ask students to simplify an expression by combining terms and combining exponents, adding exponents when multiplying terms with the same base, subtracting exponents when dividing terms with the same base, and multiplying exponents when one term with an exponent is raised to another exponent. Some questions may ask students to identify equivalent forms of an expression written in a more complex form than the provided one. Exponent questions appear on approximately 1.3% of the Digital SAT. Exponents fall under Advanced Math according to the College Board. 

Table of Contents

Exponents Lesson

The lesson covers the types of exponents questions that show up on the Digital SAT. Concepts in this lesson include how to multiply terms that have exponents, how to divide terms that have exponents, how to raise an expression with an exponent to an exponent, what having an exponent of 0 means, what negative exponents mean, and what fractions in exponents mean.

What Do Exponents Questions Look Like?

Here are some examples of Exponents questions from the Digital SAT.

  • Which expression is equivalent to (m^4q^4z^{-1})(mq^5z^3), where m, q, and z are positive?
  • If 4^{8c}=\sqrt[3]{4^7}, what is the value of c?

1. How to Multiply Terms That Have Exponents

When you multiply terms that have the same base, you add exponents.

x^2\times x^5=x^7

Here is a more complicated one

x^2 y^3 z \times xy^5 z^4

If there is no exponent written, there is an exponent of 1. That is true for one z in the first term and for the x in the second term.

Therefore,

x^2 y^3 z \times xy^5 z^4 = x^3y^8z^5

2. How to Divide Terms That Have Exponents

When you divide terms that have the same base, you subtract exponents.

\dfrac{x^8}{x^3}=x^5

Here is a more complicated one

\dfrac{x^5 y^3 z^4}{x^2y^3z}

The y^3 terms in the numerator and denominator cancel out. The other exponents subtract.

x^3z^3

3. How to Raise an Expression with an Exponent to an Exponent

When you raise an expression with exponents to another power, you multiply the exponents.

Example

Simplify the expression below.

(a^3 b^2 c^8 )^3

becomes

a^9b^6c^{24}

4. What Does Having an Exponent of 0 Mean?

Any number raised to zero is 1.

x^0=1

Also

(\dfrac{x^2 y^3-32}{4x^5-3z^2 })^0=1

There are a lot of terms, but the entire expression is raised to 0, so it is equal to 1.

Be careful.

xy^0=x(1)=x

In this example, only the y is raised to 0, so y^0 becomes 1. The x remains x.

5. What Do Negative Exponents Mean?

Think of a negative exponent as a sign that the term is in the wrong spot. If it is in the numerator, move it to the denominator and make the exponent positive. If it is in the denominator, move it to the numerator and make it positive.

Example

\dfrac{x^2 y^3}{a^{-4} b^2 }

In the example above, the exponent for the a is negative, so move it to the numerator.

\dfrac{a^4 x^2 y^3}{b^2}

Example

Here is another example

\dfrac{2x^{-4} y^2}{z^3}

Only the x has a negative exponent, so only the x should move to the denominator with its exponent. Do not move the coefficient, 2.

Moving the 2 along with the x is a common mistake.

We would end up with
\dfrac{2y^2}{x^4 z^3}

6. What Do Fractions in Exponents Mean?

A fraction in the exponent represents a root, such as a square root or cubed root.

x^{\frac{1}{2}}=\sqrt{x},

x^{\frac{1}{3}}=\sqrt[3]{x},

x^{\frac{1}{4}}=\sqrt[4]{x}

The denominator of the exponent represents the root.

It is possible for the numerator to be a number other than 1. Treat the numerator like a regular exponent.

x^{\frac{4}{3}}=\sqrt[3]{x^4}

The 4 in the numerator means to the 4th power. The 3 in the denominator means cubed root.

Example

Rewrite x^{\frac{5}{2}} with an integer power and root.

Explanation & Solution

5 is the power, and 2 is the root

x^{\frac{5}{2}}=\sqrt{x^5}

Digital SAT Exponent Question Tips

  1. Product Rule: a^m \times a^n = a^{m+n}
  2. Quotient Rule: \dfrac{a^m}{a^n} = a^{m-n} (a ≠ 0)
  3. Power Rule: (a^m)^n = a^{mn}
  4. Power of a Product: (ab)^m = a^m \times b^m
  5. Power of a Quotient: (\dfrac{a}{b})^m = \dfrac{a^m}{b^m}
  6. Zero Exponent: a^0 = 1 (a ≠ 0)
  7. Negative Exponent: a^{-n} = \dfrac{1}{a^n}
  8. Fractional Exponent: a^{\dfrac{m}{n}} = \sqrt[n]{a^m}

Example

Which expression is equivalent to (m^5n^2)(m^{-3}n^4), where m and n are positive?

A) m^2n^6
B) m^8n^6
C) m^2n^8
D) m^{-15}n^8

Video Explanation

Text Explanation

Answer: A

Use the product property of exponents: when multiplying powers with the same base, add the exponents.

(m^5)(m^{-3})=m^{5+(-3)}=m^2,
(n^2)(n^4)=n^{2+4}=n^6
Therefore,
(m^5n^2)(m^{-3}n^4)=m^2n^6

So the correct answer is A.

Practice Problems with Video Explanations

Here is a set of practice Digital SAT Exponents practice problems. After selecting an answer, press “See Answer” to see the correct answer and a video explanation showing how to properly solve the questions. At the end of the set, after you press “Submit”, you’ll be able to see all of the questions, answers, and video explanations to review.

For more practice like this, enroll in our on-demand SAT prep course here: https://caddellprep.com/sat/prep/on-demand/

1. Which expression is equivalent to (p^5q^{-4})(p^{-2}q^7), where p and q are positive?

Question 1 of 3

2. Which expression is equivalent to x^{7/9}, where x>0?

Question 2 of 3

3. The expression 8\sqrt[3]{27x^4}\sqrt[4]{16x^3} is equivalent to ax^b, where a and b are positive constants and x>1. What is the value of a+b?

Question 3 of 3


 

Common Mistakes

Two common mistakes students make when answering exponent questions occur when terms with the same base are multiplied: multiplying exponents when they should be added and multiplying the bases.

Multiplying Exponents When They Should be Added

A common mistake for questions that involve multiplying terms that have exponents and the same base, is to multiply the exponents instead of adding them.

For example, a student may incorrectly simplify 5^4\times 5^3 as 5^{12}, but the correct answer is 5^7.

Multiplying the Bases When Only the Exponents Should be Added

A common mistake for questions that involve multiplying terms that have exponents and the same base, is to multiply the bases also.

For example, a student may incorrectly simplify 5^4\times 5^3 as 25^7, but the correct answer is 5^7, the base should remain unchanged.

Related Topics

Solving for a variable in terms of others and functions are topics related to exponents.

Solving for a Variable in Terms of Others

Exponent questions can involve solving for a variable in terms of another. For example, students may need to rearrange an equation that includes exponents or isolate a variable that appears in an exponential expression. These questions require students to understand both inverse operations and exponent rules. Therefore, practicing solving for a variable in terms of others can help students answer more advanced exponent questions.

Functions

Exponents often appear in function questions. For example, a function may include a term with an exponent, and students may need to evaluate the function for a specific input value. In these questions, students need to follow the correct order of operations and simplify the exponent before completing the rest of the calculation. Therefore, practicing evaluating functions can help students improve on exponent questions.

All Math Topics

All of our math topics are available here: https://caddellprep.com/sat/math/ for you to review and improve on your SAT. There are lessons, practice problems, and video explanations for you. If you need more help, try our on-demand SAT course with video lessons, practice tests, and sets of questions for each topic: https://caddellprep.com/sat/prep/on-demand/

Glyn Caddell - Founder of Caddell Prep

Glyn Caddell

Glyn Caddell holds a BS in Mechanical Engineering from NJIT and has been tutoring New York City students since 2008. He founded Caddell Prep in 2012 and is the author of Digital SAT Math Secrets: Lessons & Tricks to Quickly Improve to a Perfect 800 on the Math Test, which contains over 900 practice problems and is used in Caddell Prep’s SAT math classes. He is founding president of the Staten Island Technical High School alumni association and teaches every lesson on this site personally.