If x=a^6, y=b^6, b is not equal to 0, and a=4b, then x/y=

16 (C). We first convert each cube root to fractional exponents using "Roots as Fractional Exponents" and simplify the exponents

GMAT Exponents: If x=a^6, y=b^6, b is not equal to 0,…

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

exponentsroots

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

16 (C)