Question

simplify the radical expression.
(sqrt8{x^{8}y^{24}}=square)

Explanation:

Step1: Use radical - exponent rule

$\sqrt[n]{a^m}=a^{\frac{m}{n}}$. So, $\sqrt[8]{x^{8}y^{24}}=(x^{8}y^{24})^{\frac{1}{8}}$.

Step2: Apply power - of - a - product rule

$(ab)^n = a^n b^n$. Then $(x^{8}y^{24})^{\frac{1}{8}}=x^{8\times\frac{1}{8}}y^{24\times\frac{1}{8}}$.

Step3: Calculate exponents

$x^{8\times\frac{1}{8}}y^{24\times\frac{1}{8}}=x^{1}y^{3}=xy^{3}$.

Answer:

$xy^{3}$