If m = \sqrt[3]{p^{9}} , n = \sqrt[3]{q^{9}} , q is not equal to 0, and p = 3q, then \frac{m}{n} =

If m = \sqrt[3]{p^{9}} , n = \sqrt[3]{q^{9}} , q i... | Free GMAT Practice Question | GMAT Panda

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GMAT Quant — Algebra (Exponents)

If m = 3 p^{9}, n = 3 q^{9}, q is not equal to 0, and p = 3 q, then \frac{m}{n} =

Explanation	Calculations	Help
$We first convert each cube root to fractional exponents using "Roots as Fractional Exponents" and simplify the exponents$	$m = p^{9 \times \frac{1}{3}} = p^{3} n = q^{9 \times \frac{1}{3}} = q^{3}$	Theory & Tactics Method Card ROOT2 Click to view full details
$We form the ratio and rewrite it as a power of a fraction using "Exponents of Fractions"$	$\frac{m}{n} = \frac{p ^{3}}{q ^{3}} (\frac{p}{q})^{3}$	Theory & Tactics Method Card EXP0-B Click to view full details
$We substitute "p = 3q" into the expression and calculate the cube$	$(\frac{p}{q})^{3} = (\frac{3 q}{q})^{3} = 3^{3} = 27$

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B

GMAT Quant — Algebra (Exponents)

If m = 3 p^{9}, n = 3 q^{9}, q is not equal to 0, and p = 3 q, then \frac{m}{n} =

Explanation	Calculations	Help
$We first convert each cube root to fractional exponents using "Roots as Fractional Exponents" and simplify the exponents$	$m = p^{9 \times \frac{1}{3}} = p^{3} n = q^{9 \times \frac{1}{3}} = q^{3}$	Theory & Tactics Method Card ROOT2 Click to view full details
$We form the ratio and rewrite it as a power of a fraction using "Exponents of Fractions"$	$\frac{m}{n} = \frac{p ^{3}}{q ^{3}} (\frac{p}{q})^{3}$	Theory & Tactics Method Card EXP0-B Click to view full details
$We substitute "p = 3q" into the expression and calculate the cube$	$(\frac{p}{q})^{3} = (\frac{3 q}{q})^{3} = 3^{3} = 27$

Scroll horizontally to view all columns

B