Respuesta :

gmany

[tex]0.125=\dfrac{125}{1,000}=\dfrac{1}{8}\\\\\dfrac{1}{8}=\dfrac{1}{2^3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\\dfrac{1}{2^3}=2^{-3}\\-----------------\\\\\text{The equation:}\\\\(0.125)^4=2^n\\\\\left(2^{-3}\right)^4=2^n\qquad\text{use}\ (a^n)^m=a^{n\cdot m}\\\\2^{(-3)(4)}=2^n\\\\2^{-12}=2^n\iff\boxed{n=-12}[/tex]

abidemiokin

The required integer n for which (0.125)^4 equal to 2^n is -12

In order to determine the value of "n", we will equate both expressions to have;

(0.125)^4 = 2^n

This can also be written as:

[tex](2^{-3})^4 =2 ^n\\2^{-12} = 2^n[/tex]

Cancel the base and equate the power to have:

[tex]n = -12[/tex]

Hence the required integer n for which (0.125)^4 equal to 2^n is -12

Learn more on indices here: https://brainly.com/question/10339517

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