The rules that solve most questions
- Multiply same-base powers: add exponents. xᵃ · xᵇ = xᵃ⁺ᵇ.
- Divide same-base powers: subtract exponents. xᵃ / xᵇ = xᵃ⁻ᵇ.
- Power of a power: multiply exponents. (xᵃ)ᵇ = xᵃᵇ.
- Power of a product: apply the exponent to every factor, including the number. (2x³)² = 4x⁶.
- Quick check: plug in x = 2 to both the original and a choice; equivalent expressions give the same value.
Traps the wrong answers are built on
- Multiplying exponents when you should add them, or the reverse.
- Raising the variable to the power but not the coefficient.
Worked example
Which expression is equivalent to (4x³)³?
- A. 12x⁹
- B. 4x⁹
- C. 64x⁶
- D. 64x⁹
Answer: D. Raise each factor to the power 3: 4³ = 64. For the variable, multiply the exponents: (x³)³ = x⁹. So the expression equals 64x⁹.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Medium
Which expression is equivalent to (4x³)³?
Show answer and explanation
Answer: D
Raise each factor to the power 3: 4³ = 64.
For the variable, multiply the exponents: (x³)³ = x⁹.
So the expression equals 64x⁹.
- Question 2Medium
Which expression is equivalent to (5x³)³?
Show answer and explanation
Answer: D
Raise each factor to the power 3: 5³ = 125.
For the variable, multiply the exponents: (x³)³ = x⁹.
So the expression equals 125x⁹.
- Question 3Medium
Which expression is equivalent to (2x⁴)³?
Show answer and explanation
Answer: A
Raise each factor to the power 3: 2³ = 8.
For the variable, multiply the exponents: (x⁴)³ = x¹².
So the expression equals 8x¹².
- Question 4Easier
Which expression is equivalent to (x⁷ · x⁹) / x¹⁵, where x > 0?
Show answer and explanation
Answer: A
When you multiply powers of the same base, add the exponents: x⁷ · x⁹ = x¹⁶.
When you divide, subtract: x¹⁶ / x¹⁵ = x¹.
- Question 5Easier
Which expression is equivalent to (x⁹ · x⁴) / x³, where x > 0?
Show answer and explanation
Answer: C
When you multiply powers of the same base, add the exponents: x⁹ · x⁴ = x¹³.
When you divide, subtract: x¹³ / x³ = x¹⁰.
- Question 6Easier
Which expression is equivalent to (x⁵ · x⁸) / x¹¹, where x > 0?
Show answer and explanation
Answer: D
When you multiply powers of the same base, add the exponents: x⁵ · x⁸ = x¹³.
When you divide, subtract: x¹³ / x¹¹ = x².
- Question 7Medium
Which expression is equivalent to (3x⁶)²?
Show answer and explanation
Answer: C
Raise each factor to the power 2: 3² = 9.
For the variable, multiply the exponents: (x⁶)² = x¹².
So the expression equals 9x¹².
- Question 8Medium
Which expression is equivalent to (3x³)²?
Show answer and explanation
Answer: B
Raise each factor to the power 2: 3² = 9.
For the variable, multiply the exponents: (x³)² = x⁶.
So the expression equals 9x⁶.
- Question 9Medium
Which expression is equivalent to (5x⁶)²?
Show answer and explanation
Answer: C
Raise each factor to the power 2: 5² = 25.
For the variable, multiply the exponents: (x⁶)² = x¹².
So the expression equals 25x¹².
- Question 10Easier
Which expression is equivalent to (x⁶ · x⁶) / x¹¹, where x > 0?
Show answer and explanation
Answer: C
When you multiply powers of the same base, add the exponents: x⁶ · x⁶ = x¹².
When you divide, subtract: x¹² / x¹¹ = x¹.
More Advanced Math practice
Questions people ask
Is this equivalent expressions practice like the real SAT?
The questions follow the format of the digital SAT's Advanced Math domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Advanced Math is one of the four content domains of the SAT Math section, alongside Algebra, Problem-Solving and Data Analysis, Geometry and Trigonometry.