Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }$$
A) $x ^ { 4 } y ^ { 16 / 3 }$
B) $x ^ { 8 / 3 } y ^ { 16 / 3 }$
C) $x ^ { 14 / 3 } y ^ { 26 / 3 }$
D) $\frac { 2 } { 3 } x ^ { 4 } y ^ { 8 }$

Question

Quizplus · Accepted Answer

To simplify $\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }$, apply the power of a product rule, which states that $(ab)^n = a^n b^n$. Thus, $x^{4(2/3)}y^{8(2/3)} = x^{8/3}y^{16/3}$.

Simplify the Expression by Using the Properties of Rational Exponents (x4y8)2/3\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }(x4y8)2/3

Simplify the Expression by Using the Properties of Rational Exponents $\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }$