Write the Fraction in Simplest Form (15m^-7)/(3(m^-2)^4)

$\frac{15 m^{- 7}}{3 {(m^{- 2})}^{4}}$

Move $m^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{15}{3 {(m^{- 2})}^{4} m^{7}}$

Cancel the common factor of $15$ and $3$ .

Factor $3$ out of $15$ .

$\frac{3 \cdot 5}{3 {(m^{- 2})}^{4} m^{7}}$

Cancel the common factors.

Factor $3$ out of $3 {(m^{- 2})}^{4} m^{7}$ .

$\frac{3 \cdot 5}{3 ({(m^{- 2})}^{4} m^{7})}$

Cancel the common factor.

$\frac{3 \cdot 5}{3 ({(m^{- 2})}^{4} m^{7})}$

Rewrite the expression.

$\frac{5}{{(m^{- 2})}^{4} m^{7}}$

Simplify the denominator.

Multiply the exponents in ${(m^{- 2})}^{4}$ .

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

$\frac{5}{m^{- 2 \cdot 4} m^{7}}$

Multiply $- 2$ by $4$ .

$\frac{5}{m^{- 8} m^{7}}$

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

$\frac{5}{\frac{1}{m^{8}} m^{7}}$

Combine $\frac{1}{m^{8}}$ and $m^{7}$ .

$\frac{5}{\frac{m^{7}}{m^{8}}}$

Reduce the expression $\frac{m^{7}}{m^{8}}$ by cancelling the common factors.

Multiply by $1$ .

$\frac{5}{\frac{m^{7} \cdot 1}{m^{8}}}$

Factor $m^{7}$ out of $m^{8}$ .

$\frac{5}{\frac{m^{7} \cdot 1}{m^{7} m}}$

Cancel the common factor.

$\frac{5}{\frac{m^{7} \cdot 1}{m^{7} m}}$

Rewrite the expression.

$\frac{5}{\frac{1}{m}}$

Multiply the numerator by the reciprocal of the denominator.

$5 m$