How do you write #(-2x)^-4# with positive exponents?

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Answer 1 · 2018-03-25T06:39:28

This is a law of exponents
#a^(-m)=1/a^m#

Then...
#(-2x)^-4=1/(-2x)^4#

This is also a law of exponents
#(ab)^m=a^mb^m#

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

But.. as you said you wanted it with positive exponent... this step won't be necessary

Answer 2 · 2018-03-25T06:42:37

It is equal to #1/(16x^4)#.

Use these two exponents rules:

#color(blue)x^-color(red)m=1/color(blue)x^color(red)m#

#(color(blue)xcolor(green)y)^color(red)m=color(blue)x^color(red)mcolor(green)y^color(red)m#

Here are these two rules applied to our problem:

#color(white)=(-2x)^-4#

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

#=1/(-2*x)^4#

#=1/((-2)^4*x^4)#

#=1/((-1*2)^4*x^4)#

#=1/((-1)^4*2^4*x^4)#

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

#=1/(1*16*x^4)#

#=1/(16*x^4)#

#=1/(16x^4)#