Question

Rewrite the following as an expotential expression in simplest forn.

Answer 1

The rule of exponents:

`\begin{gathered} ^m\sqrt[]{x^n}=x^{(n)/(m)} \\ x^n=(1)/(x^(-n)) \end{gathered}`

The given expression is,

`^3\sqrt[]{(x^6)/(x^(-15))}`

Rewrite the above expression as an exponential expression,

`\begin{gathered} ((x^6)/(x^(-15)))^{(1)/(3)} \\ =(x^6x^(15))^{(1)/(3)} \\ =(x^(6+15))^{(1)/(3)} \\ =(x^(21))^{(1)/(3)} \\ =x^{(21)/(3)} \\ =x^7 \end{gathered}`

Therefore, the simplest exponential form of the given expression is,

`x^7`