Question

Help! im doing a gooru question but i dont know how to do it

Answer 1

`4a^(10)`

Explanation:

`\textsf{Given expression}:`

`(a^2)^5 \cdot 4^3 \cdot 4^(-2)`

`\textsf{Apply radical rule} \quad a^b \cdot a^c=a^(b+c):`

`\implies (a^2)^5 \cdot 4^(3+(-2))`

`\implies (a^2)^5 \cdot 4^1`

`\implies (a^2)^5 \cdot 4`

`\textsf{Apply radical rule} \quad (a^b)^c=a^(bc):`

`\implies a^(2 \cdot 5) \cdot 4`

`\implies a^(10) \cdot 4`

`\textsf{Final solution}:`

`\implies 4a^(10)`