For x > 0, which expression is equivalent to x^32?

SAT Equivalent expressions Practice Question 10 (Medium)

SAT Owl

Question bank / Equivalent expressions

Math · Advanced MathMedium

For $x > 0$ , which expression is equivalent to $x^{\frac{3}{2}}$ ?

$\sqrt{x^3}$

$\sqrt[3]{x^2}$

$\frac{x^3}{2}$

$\frac{3x}{2}$

Show answer and explanation

Answer: A

A rational exponent $\frac{m}{n}$ means the $n$ th root of the $m$ th power: $x^{\frac{m}{n}} = \sqrt[n]{x^m}$ . So $x^{\frac{3}{2}} = \sqrt{x^3}$ .

Choice B switches the roles of the numerator and denominator of the exponent.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.