Question

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

Answer 1

`-(81v^4)/t^4`

Explanation:

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

`-(-t/(3v))^-4`

Note that in indices `a^-m = 1/a^m`

`- (-1/(t/(3v)))^4`

`-(-1 div t/(3v))^4`

`- (-1 xx (3v)/t)^4`

`-((-3v)/t)^4`

`-((-3v)^4/t^4)`

`-((-3v xx -3v xx -3v xx -3v)/t^4)`

Recall `-> (- xx - = +)`

`:. -(+(81v^4)/t^4)`

Also `-> (- xx + = -)`

`rArr -(81v^4)/t^4 -> Answer`

Answer 2

`-(81v^4)/t^4`

Explanation:

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

`(a/b)^-m = (b/a)^m`

`-(-t/(3v))^color(blue)(-4) = -(-(3v)/t)^color(blue)(4)`

A negative raised to an even power makes a positive.

`= -((81v^4)/t^4)`

`-(81v^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.