If x=\sqrt[3]{a^{6}}, y=\sqrt[3]{b^{6}}, b is not equal to 0, and a=4b, then \frac{x}{y}=

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GMAT Quant — Algebra (Exponents)

If x = 3 a^{6}, y = 3 b^{6}, b is not equal to 0, and a = 4 b, then \frac{x}{y} =

Explanation	Calculations	Help
$We first convert each cube root to fractional exponents using "Roots as Fractional Exponents" and simplify the exponents$	$x = a^{6 \times \frac{1}{3}} = a^{2} y = b^{6 \times \frac{1}{3}} = b^{2}$	Theory & Tactics Method Card ROOT2 Click to view full details
$We form the ratio and rewrite it as a power of a fraction using "Exponents of Fractions"$	$\frac{x}{y} = \frac{a ^{2}}{b ^{2}} (\frac{a}{b})^{2}$	Theory & Tactics Method Card EXP0-B Click to view full details
$We substitute "a = 4 b" into the expression and calculate the square$	$(\frac{a}{b})^{2} = (\frac{4 b}{b})^{2} = 4^{2} 4^{2} = 16$

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C

GMAT Quant — Algebra (Exponents)

If x = 3 a^{6}, y = 3 b^{6}, b is not equal to 0, and a = 4 b, then \frac{x}{y} =

Explanation	Calculations	Help
$We first convert each cube root to fractional exponents using "Roots as Fractional Exponents" and simplify the exponents$	$x = a^{6 \times \frac{1}{3}} = a^{2} y = b^{6 \times \frac{1}{3}} = b^{2}$	Theory & Tactics Method Card ROOT2 Click to view full details
$We form the ratio and rewrite it as a power of a fraction using "Exponents of Fractions"$	$\frac{x}{y} = \frac{a ^{2}}{b ^{2}} (\frac{a}{b})^{2}$	Theory & Tactics Method Card EXP0-B Click to view full details
$We substitute "a = 4 b" into the expression and calculate the square$	$(\frac{a}{b})^{2} = (\frac{4 b}{b})^{2} = 4^{2} 4^{2} = 16$

Scroll horizontally to view all columns

C