Question

How do I simplify this?
`(4{a}^(3) {b}^( - 2) {)}^(2)`

Answer 1

We can use the following properties:

`\begin{gathered} (x\cdot y\cdot z)^w=x^w\cdot y^w\cdot z^w \\ (x^y)^z=x^(yz) \end{gathered}`

Therefore:

`\begin{gathered} (4a^3b^(-2))^2=4^2\cdot a^(3\cdot2)\cdot b^(-2\cdot2)=16a^6b^(-4) \\ Finally_{\text{ }}we_{\text{ }}can_{\text{ }}use_{\text{ }}also_{\text{ }}this_{\text{ }}property: \\ a^(-n)=(1)/(a^n) \\ so: \\ 16a^6b^(-4)=(16a^6)/(b^4) \end{gathered}`