Question

n " align="absmiddle" class="latex-formula">
solve
${8}^{m} - {4}^{ - m}$
​

Answer 1

Answer:

$\displaystyle n^3-\frac{1}{n^{2}}$

Step-by-step explanation:

Exponents Properties

We need to recall the following properties of exponents:

$(a^x)^y=(a^y)^x=a^{xy}$

$\displaystyle a^{-x}=\frac{1}{a^x}$

We are given the expression:

$2^m=n$

We need to express the following expression in terms of n.

$8^m-4^{-m}$

It's necessary to modify the expression to use the given equivalence.

Recall $8=2^3 \text{ and }4 = 2^2$. Thus:

$(2^3)^m-(2^2)^{-m}$

Applying the property:

$(2^m)^3-(2^m)^{-2}$

Substituting the given expression:

$n^3-n^{-2}$

Or, equivalently:

$\mathbf{\displaystyle 8^m-4^{-m}= n^3-\frac{1}{n^{2}}}$