Question

open parentheses fraction numerator f cubed to the power of -2 end exponent over denominator h to the power of negative 1 end exponent end fraction close parentheses to the power of 4.I need this in exponential form, please.

Answer 1

First part

numerator f cubed g to the power of negative 2

The numerator can be written as

`f^3g^(-2)`

Second part

denorminator h raised to the power of negative 1

The numerator can be written as

`h^(-1)`

combining part one and two

Open parentheses fraction - fraction - close parentheses to the power of 4

This gives

`((f^3g^(-2))/(h^(-1)))^4`

simplifying the expression to remove negative exponent

Simplifying the numerator

`\begin{gathered} f^3g^(-2)=f^3* g^(-2) \\ f^3g^(-2)=f^3*(1)/(g^2) \\ f^3g^(-2)\text{ = }(f^3)/(g^2) \end{gathered}`

simplfying the denorminator

`h^(-1)\text{ = }(1)/(h)`

combining simplfied values for numerator and denorminator in the general form we have

`\begin{gathered} ((f^3g^(-2))/(h^(-1)))^4\text{ = }(((f^3)/(g^2))/((1)/(h)))^4 \\ ((f^3g^(-2))/(h^(-1)))^4=\text{ (}(f^3)/(g^2)* h)^4\text{ } \\ ((f^3g^(-2))/(h^(-1)))^4\text{ = (}(f^3h)/(g^2))^4 \end{gathered}`

Hence, the simplified form of the expression is

`((f^3h)/(g^2))^4`