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

2 Answers
Aug 3, 2017

Answer:

#-(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#

Aug 3, 2017

Answer:

#-(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.