Simplify (2m^-4)/((2m^-4)^3)

$\frac{2 m^{- 4}}{{(2 m^{- 4})}^{3}}$

Step 1

Move $m^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2}{{(2 m^{- 4})}^{3} m^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 m^{- 4}$ .

$\frac{2}{2^{3} {(m^{- 4})}^{3} m^{4}}$

Raise $2$ to the power of $3$ .

$\frac{2}{8 {(m^{- 4})}^{3} m^{4}}$

Multiply the exponents in ${(m^{- 4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2}{8 m^{- 4 \cdot 3} m^{4}}$

Multiply $- 4$ by $3$ .

$\frac{2}{8 m^{- 12} m^{4}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2}{8 \frac{1}{m^{12}} m^{4}}$

Combine exponents.

Combine $8$ and $\frac{1}{m^{12}}$ .

$\frac{2}{\frac{8}{m^{12}} m^{4}}$

Combine $\frac{8}{m^{12}}$ and $m^{4}$ .

$\frac{2}{\frac{8 m^{4}}{m^{12}}}$

Reduce the expression $\frac{8 m^{4}}{m^{12}}$ by cancelling the common factors.

Factor $m^{4}$ out of $8 m^{4}$ .

$\frac{2}{\frac{m^{4} \cdot 8}{m^{12}}}$

Factor $m^{4}$ out of $m^{12}$ .

$\frac{2}{\frac{m^{4} \cdot 8}{m^{4} m^{8}}}$

Cancel the common factor.

$\frac{2}{\frac{m^{4} \cdot 8}{m^{4} m^{8}}}$

Rewrite the expression.

$\frac{2}{\frac{8}{m^{8}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$2 \frac{m^{8}}{8}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 \frac{m^{8}}{2 (4)}$

Cancel the common factor.

$2 \frac{m^{8}}{2 \cdot 4}$

Rewrite the expression.

$\frac{m^{8}}{4}$