# How do you simplify 4(3a^4b^-2)^-1?

May 18, 2016

$4 \left(\frac{{b}^{2}}{3 {a}^{4}}\right)$

#### Explanation:

If you have a negative exponent for example ${x}^{- 1}$ it means the following:

Write as $\frac{{x}^{- 1}}{1}$ and turn upside down to give: $\frac{1}{x}$

In the same way: ${x}^{- 2} \to \frac{1}{{x}^{2}}$
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Given:$\text{ } 4 {\left(3 {a}^{4} {b}^{- 2}\right)}^{- 1}$

Dealing with the negative exponent inside the brackets first

Write as: $4 \times {\left(\frac{3 {a}^{4}}{{b}^{2}}\right)}^{-} 1$

Now dealing with the negative exponent outside the brackets

$4 \times \left(\frac{{b}^{2}}{3 {a}^{4}}\right) \to 4 \left(\frac{{b}^{2}}{3 {a}^{4}}\right)$