Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }$$
A) $x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x y ^ { 2 } }$
B) $x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x y }$
C) $x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$
D) $x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y }$

Question

Quizplus · Accepted Answer

When multiplying variables with exponents, we add the exponents. So, for $x$, we have $1+19=20$ and for $y$, we have $5+14=19$. Thus, we have $x^{20}y^{19}$ under the cube root. Taking the cube root of $x^{18}y^{18}$ gives us $x^6y^6$. Taking the cube root of the remaining $x^2y$ gives us $\sqrt[3]{x^2y}$. Thus, the final answer is $x^6y^6\sqrt[3]{x^2y}$.

Choose the One Alternative That Best Completes the Statement or Answers