simplify. (\\sqrt{x^{7}y^{4}})^{6} x^{?}y^{?}

Explanation:

Step1: Rewrite the square - root as a fractional exponent

We know that $\sqrt{a}=a^{\frac{1}{2}}$. So, $\left(\sqrt{x^{7}y^{4}}\right)^{6}=\left((x^{7}y^{4})^{\frac{1}{2}}\right)^{6}$.

Step2: Apply the power - of - a - power rule

The power - of - a - power rule is $(a^{m})^{n}=a^{mn}$. So, $\left((x^{7}y^{4})^{\frac{1}{2}}\right)^{6}=(x^{7}y^{4})^{\frac{1}{2}\times6}=(x^{7}y^{4})^{3}$.

Step3: Apply the power - of - a - product rule

The power - of - a - product rule is $(ab)^{n}=a^{n}b^{n}$. So, $(x^{7}y^{4})^{3}=x^{7\times3}y^{4\times3}$.

Step4: Calculate the exponents

$x^{7\times3}=x^{21}$ and $y^{4\times3}=y^{12}$.

Answer:

$x^{21}y^{12}$