Answer:
[tex]4a^{10}[/tex]
Step-by-step explanation:
[tex]\textsf{Given expression}:[/tex]
[tex](a^2)^5 \cdot 4^3 \cdot 4^{-2}[/tex]
[tex]\textsf{Apply radical rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies (a^2)^5 \cdot 4^{3+(-2)}[/tex]
[tex]\implies (a^2)^5 \cdot 4^1[/tex]
[tex]\implies (a^2)^5 \cdot 4[/tex]
[tex]\textsf{Apply radical rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies a^{2 \cdot 5} \cdot 4[/tex]
[tex]\implies a^{10} \cdot 4[/tex]
[tex]\textsf{Final solution}:[/tex]
[tex]\implies 4a^{10}[/tex]
