Question

Please help me thank you.

Answer 1

`\large\boxed{1.\ (4)^(-3x^2)=\left((1)/(4)\right)^(3x^2)}`

`\large\boxed{2.\ ab^(-3x)=a\left((1)/(b)\right)^(3x)=a\left[\left((1)/(b)\right)^3\right]^x}`

Explanation:

`Use:\ a^(-n)=\left((1)/(a)\right)^n\\------------\\\\(4)^(-3x^2)=\left[(4)^(-1)\right]^(3x^2)=\left((1)/(4)\right)^(3x^2)`

`Use:\ a^(-n)=\left((1)/(a)\right)^n\ and\ (a^n)^m=a^(nm)\\--------------------\\\\ab^(-3x)=a\cdot b^(-3x)=a\left[(b)^(-1)\right]^(3x)=a\left((1)/(b)\right)^(3x)\\\\ab^(-3x)=a\left((1)/(b)\right)^(3x)=a\left[\left((1)/(b)\right)^3\right]^x`