Answer:
The expression equivalent to [tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex] is [tex]\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex] ⇒ C
Step-by-step explanation:
Let us use the exponent rule [tex](a^{m})^{n}[/tex] = [tex]a^{m.n}[/tex]
∵ The expression is [tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex]
→ By using the rule above multiply the power of each letter by 4
∵ [tex](m^{5})^{4}[/tex] = [tex]m^{20}[/tex]
∵ [tex](n^{1})^{4}[/tex] = [tex]n^{4}[/tex]
∵ [tex](p^{1})^{4}[/tex] = [tex]p^{4}[/tex]
∵ [tex](q^{2})^{4}[/tex] = [tex]q^{8}[/tex]
→ Substitute them in the expression above
∴ [tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex] = [tex]\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex]
∴ The expression equivalent to [tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex] is [tex]\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex]
