simplify. \n$sqrt5{x^{10}y^{30}z^{25}}$ \n$x^{?}y^{ }z^{ }$

Explanation:

Step1: Apply root - exponent rule

Use the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. For $\sqrt[5]{x^{10}y^{30}z^{25}}$, we can rewrite it as $(x^{10}y^{30}z^{25})^{\frac{1}{5}}$.

Step2: Apply power - of - a - product rule

According to $(ab)^n=a^n b^n$, we have $(x^{10}y^{30}z^{25})^{\frac{1}{5}}=x^{10\times\frac{1}{5}}y^{30\times\frac{1}{5}}z^{25\times\frac{1}{5}}$.

Step3: Calculate exponents

$10\times\frac{1}{5} = 2$, $30\times\frac{1}{5}=6$, $25\times\frac{1}{5}=5$. So $x^{10\times\frac{1}{5}}y^{30\times\frac{1}{5}}z^{25\times\frac{1}{5}}=x^{2}y^{6}z^{5}$.

Answer:

$x^{2}y^{6}z^{5}$