If 2^a = 8 and 2^b = 32, what is a + b?

C. 8. Since 8 = 2^3 and 32 = 2^5, a = 3 and b = 5, so a + b = 8.

SAT Math skill page

SAT Exponent Rules Practice

Use exponent rules to simplify expressions, compare powers, and avoid common sign traps.

Practice exponent rules in Dolphin SAT Practice questions

10-16 min practice time3 questions in practice blockAdvanced Math

Practice time10-16 min

Practice questions3 questions

Best forAdvanced Math

What this tests

What to know for this SAT skill

Apply product and quotient rules for exponents
Simplify powers raised to powers
Interpret negative and zero exponents
Connect radicals to fractional exponents

Dolphin practice questions

Practice your skill

Question 1 of 3Easy

Which expression is equivalent to

x^{3}

x^{4}

$x^{7}$
$x^{1} 2$
$2 x^{7}$
x

Show answer and solution

Correct answer $A . x^{7}$

Solution walkthrough

When multiplying powers with the same base, add the exponents: 3 + 4 = 7.

Question 2 of 3Medium

2^{a}

= 8 and

2^{b}

= 32, what is a + b?

Show answer and solution

Correct answerC. 8

Solution walkthrough

Since 8 = $2^{3}$ and 32 = $2^{5}$ , a = 3 and b = 5, so a + b = 8.

Question 3 of 3Hard

Which expression is equivalent to (

x^{2} y

^-3)^2?

$x^{4} y^{-} 6$
$x^{4} y^{6}$
$x^{2} y^{-} 6$
$x^{4} / y^{-} 6$

Show answer and solution

Correct answer $A . x^{4} y^{-} 6$

Solution walkthrough

Raise each factor to the second power: ( $x^{2}$ )^2 = $x^{4}$ and (y^-3)^2 = y^-6.

Avoid these traps

Common mistakes on this skill

Adding exponents during addition

Exponents add when multiplying powers with the same base, not when adding the powers themselves.

Applying a power to only one factor

A power outside parentheses applies to every factor inside and multiplies existing exponents.

Study plan

How to practice this skill in Dolphin

Dolphin Web gives you a personalized SAT study plan with lessons, unlimited Pip AI help, practice questions, full-length tests, and mistake review. The iPhone and Android apps are free. See plans.

Identify whether the operation is multiplication, division, or a power of a power.
Apply one exponent rule at a time while keeping the base unchanged where required.
Rewrite negative or fractional exponents and check the result with a simple positive base.

Practice exponent rules in Dolphin SAT

Related practice

Build the surrounding skills

Skill cluster

Keep practicing SAT Math

FAQ

Questions about SAT Exponent Rules Practice

What does a negative exponent mean?

For a nonzero base, a^-n equals 1 divided by a^n.

When do exponents multiply?

They multiply in a power of a power, such as (x^a)^b = x^(ab).