For x 0, which expression is equivalent to x^52x? | SAT Equivalent expressions Question, Answer Explained

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Math · Advanced MathMedium

For $x > 0$ , which expression is equivalent to $\frac{x^{\frac{5}{2}}}{\sqrt{x}}$ ?

$x^{\frac{5}{4}}$

$x^2$

$x^3$

$x^5$

Show answer and explanation

Answer: B

Write $\sqrt{x}$ as $x^{\frac{1}{2}}$ . When dividing powers with the same base, subtract the exponents: $x^{\frac{5}{2} - \frac{1}{2}} = x^{\frac{4}{2}} = x^2$ .

Choice C adds the exponents, which is the rule for multiplying powers, not dividing them.

Why the other choices are wrong

A. This multiplies the exponents 5/2 and 1/2. For division, subtract the exponents.
C. This adds the exponents, which is the rule for multiplication. For division, subtract them.
D. This divides 5/2 by 1/2. For division of powers, subtract the exponents.

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