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:

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