Simplify. Assume that all variables represent positive real numbers.
-$$\frac { \sqrt [ 3 ] { 625 x ^ { 17 } y ^ { 16 } } } { \sqrt [ 3 ] { 5 x ^ { 5 } y ^ { 2 } } }$$
A) $25 x ^ { 6 } y ^ { 3 } \sqrt [ 3 ] { y }$
B) $10 x ^ { 4 } y ^ { 5 }$
C) $5 x ^ { 4 } y ^ { 4 } \sqrt [ 3 ] { y ^ { 2 } }$
D) $5 x ^ { 3 } y ^ { 4 } \sqrt [ 3 ] { x ^ { 2 } }$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the cube root by dividing the numerator by the denominator: $\frac{625x^{17}y^{16}}{5x^5y^2} = 125x^{12}y^{14}$. Then, take the cube root: $\sqrt[3]{125x^{12}y^{14}} = 5x^4y^{4}\sqrt[3]{y^2}$, which matches choice C.

Simplify Assume That All Variables Represent Positive Real Numbers 625x17y1635x5y23\frac { \sqrt [ 3 ] { 625 x ^ { 17 } y ^ { 16 } } } { \sqrt [ 3 ] { 5 x ^ { 5 } y ^ { 2 } } }35x5y2​3625x17y16​​

Simplify Assume That All Variables Represent Positive Real Numbers $\frac { \sqrt [ 3 ] { 625 x ^ { 17 } y ^ { 16 } } } { \sqrt [ 3 ] { 5 x ^ { 5 } y ^ { 2 } } }$