Simplify the expression (( 5)^y)^2( 5)^9 5^y5^9

Simplify the expression (( 5)^y)^2( 5)^9 5^y5… | GMAT Sprint

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555-605

Algebra

Simplify the expression $\frac{\frac{((\sqrt{5})^y)^2}{(\sqrt{5})^{9}}}{\frac{5^y}{5^{9}}}$

Answer Choices

Correct answer marked below

5

5^2

5^{9/2}

Correct

5^{11/2}

5^9

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Explanation

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Official Explanation

Official

To simplify the expression

\frac{\frac{((\sqrt{5})^y)^2}{(\sqrt{5})^{9}}}{\frac{5^y}{5^{9}}}

, we start by simplifying the numerator and the denominator separately.

Numerator:

- The numerator is

(\sqrt{5})^{2y} / (\sqrt{5})^{9}

.

- We can rewrite

(\sqrt{5})^{2y}

(5^{1/2})^{2y} = 5^{y}

.

- Thus, the numerator becomes

\frac{5^{y}}{(\sqrt{5})^{9}} = \frac{5^{y}}{(5^{1/2})^{9}} = \frac{5^{y}}{5^{9/2}} = 5^{y - 9/2}

.…

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Comments

KARTIKFeb 5, 2025

Amazing

SallyMar 13, 2025

Great

EdoardoJan 30, 2025

greatt question!

ShivamMar 1, 2025

Great explanation

MapJun 27, 2024

Great

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Simplify the expression ((5)y)2(5)95y59\frac{\frac{((\sqrt{5})^y)^2}{(\sqrt{5})^{9}}}{\frac{5^y}{5^{9}}}595y​(5​)9((5​)y)2​​