which expression is equivalent to $\\left(\\frac{m^{5}n}{pq^{2}}\\right)^{4}$?\n$\\frac{m^{9}n^{5}}{p^{5}q^{6…

which expression is equivalent to $\\left(\\frac{m^{5}n}{pq^{2}}\\right)^{4}$?\n$\\frac{m^{9}n^{5}}{p^{5}q^{6}}$\n$\\frac{m^{20}n^{4}}{pq^{2}}$\n$\\frac{m^{20}n^{4}}{p^{4}q^{8}}$\n$\\frac{m^{9}n^{4}}{p^{4}q^{6}}$

which expression is equivalent to $\\left(\\frac{m^{5}n}{pq^{2}}\\right)^{4}$?\n$\\frac{m^{9}n^{5}}{p^{5}q^{6}}$\n$\\frac{m^{20}n^{4}}{pq^{2}}$\n$\\frac{m^{20}n^{4}}{p^{4}q^{8}}$\n$\\frac{m^{9}n^{4}}{p^{4}q^{6}}$

Answer

Explanation:

Step1: Apply power - of - a - quotient rule

$(\frac{m^{5}n}{pq^{2}})^{4}=\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}$

Step2: Apply power - of - a - product rule

For the numerator $(m^{5}n)^{4}=m^{5\times4}n^{4}=m^{20}n^{4}$, and for the denominator $(pq^{2})^{4}=p^{4}(q^{2})^{4}=p^{4}q^{2\times4}=p^{4}q^{8}$

Step3: Write the final equivalent expression

So, $\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}=\frac{m^{20}n^{4}}{p^{4}q^{8}}$

Answer:

$\frac{m^{20}n^{4}}{p^{4}q^{8}}$ (corresponding to the third option in the multiple - choice list)