# How do you simplify -(-t/(3v))^-4?

Aug 3, 2017

$- \frac{81 {v}^{4}}{t} ^ 4$

#### Explanation:

Another method or way of solving this is as follows; Using BODMAS

$- {\left(- \frac{t}{3 v}\right)}^{-} 4$

Note that in indices ${a}^{-} m = \frac{1}{a} ^ m$

$- {\left(- \frac{1}{\frac{t}{3 v}}\right)}^{4}$

$- {\left(- 1 \div \frac{t}{3 v}\right)}^{4}$

$- {\left(- 1 \times \frac{3 v}{t}\right)}^{4}$

$- {\left(\frac{- 3 v}{t}\right)}^{4}$

$- \left({\left(- 3 v\right)}^{4} / {t}^{4}\right)$

$- \left(\frac{- 3 v \times - 3 v \times - 3 v \times - 3 v}{t} ^ 4\right)$

Recall $\to \left(- \times - = +\right)$

$\therefore - \left(+ \frac{81 {v}^{4}}{t} ^ 4\right)$

Also $\to \left(- \times + = -\right)$

$\Rightarrow - \frac{81 {v}^{4}}{t} ^ 4 \to A n s w e r$

Aug 3, 2017

$- \frac{81 {v}^{4}}{t} ^ 4$

#### Explanation:

The index is negative. This can be changed to a positive using the following law:

${\left(\frac{a}{b}\right)}^{-} m = {\left(\frac{b}{a}\right)}^{m}$

$- {\left(- \frac{t}{3 v}\right)}^{\textcolor{b l u e}{- 4}} = - {\left(- \frac{3 v}{t}\right)}^{\textcolor{b l u e}{4}}$

A negative raised to an even power makes a positive.

$= - \left(\frac{81 {v}^{4}}{t} ^ 4\right)$

$- \frac{81 {v}^{4}}{t} ^ 4$

Note that there were actually five negative signs in the expression (excluding the one in the index which has a different meaning) - the result has to be negative.