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

1 Answer

Answer:

#1/(8x^3)#

Explanation:

#(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)#