Simplify #(16x^4)^(-3/4)# using only positive exponents?

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Answer 1 · 2017-10-28T01:08:17

#1/(8x^3)#

#(16x^4)^(-3/4)#

There are a few things going on here so let's do them one at a time.

The negative sign in the exponent

#x^-1=1/x#

So let's rewrite our expression:

#(16x^4)^(-3/4)=1/(16x^4)^(3/4)#

Taking the 4th root

Next let's note that #16=2^4# and so we can write:

#1/(16x^4)^(3/4)=1/(2^4x^4)^(3/4)#

and from here we can take the 4th root:

#1/(2^4x^4)^(3/4)=1/(2x)^3#

Cube the denominator

#1/(2x)^3=1/(8x^3)#