Use rational exponents to simplify the radical. Assume that all variables represent positive real numbers.
-$\sqrt [ 10 ] { x ^ { 8 } y ^ { 8 } }$
A) $\sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } }$
B) $\sqrt [ 5 ] { x ^ { 4 } y }$
C) $\sqrt [ 5 ] { x y ^ { 4 } }$
D) $\sqrt { x ^ { 4 } y ^ { 4 } }$

Question

Quizplus · Accepted Answer

To simplify $\sqrt [ 10 ] { x ^ { 8 } y ^ { 8 } }$, we convert the radical to a rational exponent: $x^8y^8$ becomes $(x^8y^8)^{1/10}$. Simplifying the exponent, $8/10$ reduces to $4/5$, resulting in $x^{4/5}y^{4/5}$, which is equivalent to $\sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } }$.

Use Rational Exponents to Simplify the Radical x8y810\sqrt [ 10 ] { x ^ { 8 } y ^ { 8 } }10x8y8​

Use Rational Exponents to Simplify the Radical $\sqrt [ 10 ] { x ^ { 8 } y ^ { 8 } }$