If r = \sqrt[4]{p^{8}} , s = \sqrt[4]{q^{8}} , q is not equal to 0, and p = 3q, then what is \frac{r}{s}?

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GMAT Quant — Algebra (Exponents)

If r = 4 p^{8}, s = 4 q^{8}, q is not equal to 0, and p = 3 q, then what is \frac{r}{s} ?

Explanation	Calculations	Help
$We first convert each fourth root to fractional exponents using Roots as Fractional Exponents and simplify the exponents$	$r = p^{8 \times \frac{1}{4}} = p^{2} s = q^{8 \times \frac{1}{4}} = q^{2}$	Theory & Tactics Method Card ROOT2 Click to view full details
$We form the ratio and rewrite it as a power of a fraction using Exponents of Fractions$	$\frac{r}{s} = \frac{p ^{2}}{q ^{2}} (\frac{p}{q})^{2}$	Theory & Tactics Method Card EXP0-B Click to view full details
$We substitute p = 3q into the expression and calculate the square$	$(\frac{p}{q})^{2} = (\frac{3 q}{q})^{2} = 3^{2} 3^{2} = 9$

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B

GMAT Quant — Algebra (Exponents)

If r = 4 p^{8}, s = 4 q^{8}, q is not equal to 0, and p = 3 q, then what is \frac{r}{s} ?

Explanation	Calculations	Help
$We first convert each fourth root to fractional exponents using Roots as Fractional Exponents and simplify the exponents$	$r = p^{8 \times \frac{1}{4}} = p^{2} s = q^{8 \times \frac{1}{4}} = q^{2}$	Theory & Tactics Method Card ROOT2 Click to view full details
$We form the ratio and rewrite it as a power of a fraction using Exponents of Fractions$	$\frac{r}{s} = \frac{p ^{2}}{q ^{2}} (\frac{p}{q})^{2}$	Theory & Tactics Method Card EXP0-B Click to view full details
$We substitute p = 3q into the expression and calculate the square$	$(\frac{p}{q})^{2} = (\frac{3 q}{q})^{2} = 3^{2} 3^{2} = 9$

Scroll horizontally to view all columns

B