Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }$$
A) $x y \sqrt { y ^ { 4 } z ^ { 3 } }$
B) $x y z \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }$
C) $x y \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }$
D) $x \sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 3 } }$

Question

Quizplus · Accepted Answer

We can simplify the radical by breaking down each term in the radicand to its 6th power, then taking the 6th root of the perfect powers. This gives us:
$$\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } } = \sqrt [ 6 ] { x ^ { 6 } } \cdot \sqrt [ 6 ] { y ^ { 10 } } \cdot \sqrt [ 6 ] { z ^ { 3 } } = x \cdot y ^ { \frac { 10 } { 6 } } \cdot z ^ { \frac { 3 } { 6 } } = x \cdot y ^ { \frac { 5 } { 3 } } \cdot z ^ { \frac { 1 } { 2 } }$$
Simplifying the exponent of $y$, we get $y^{\frac{5}{3}} = y^{\frac{3}{3}+\frac{2}{3}} = y\sqrt[3]{y^2}$. Thus, 
$$\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } } = xy\sqrt[6]{y^4z^3}$$
which matches choice C.

Simplify the Radical Expression x6y10z36\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }6x6y10z3​

Simplify the Radical Expression $\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }$