Write the Fraction in Simplest Form (5r^-1)/(4(r^-1)^2)

$\frac{5 r^{- 1}}{4 {(r^{- 1})}^{2}}$

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

$\frac{5}{4 {(r^{- 1})}^{2} r}$

Simplify the denominator.

Multiply the exponents in ${(r^{- 1})}^{2}$ .

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

$\frac{5}{4 r^{- 1 \cdot 2} r}$

Multiply $- 1$ by $2$ .

$\frac{5}{4 r^{- 2} r}$

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

$\frac{5}{4 \frac{1}{r^{2}} r}$

Combine exponents.

Combine $4$ and $\frac{1}{r^{2}}$ .

$\frac{5}{\frac{4}{r^{2}} r}$

Combine $\frac{4}{r^{2}}$ and $r$ .

$\frac{5}{\frac{4 r}{r^{2}}}$

Reduce the expression $\frac{4 r}{r^{2}}$ by cancelling the common factors.

Factor $r$ out of $4 r$ .

$\frac{5}{\frac{r \cdot 4}{r^{2}}}$

Factor $r$ out of $r^{2}$ .

$\frac{5}{\frac{r \cdot 4}{r \cdot r}}$

Cancel the common factor.

$\frac{5}{\frac{r \cdot 4}{r \cdot r}}$

Rewrite the expression.

$\frac{5}{\frac{4}{r}}$

Multiply the numerator by the reciprocal of the denominator.

$5 \frac{r}{4}$

Combine $5$ and $\frac{r}{4}$ .

$\frac{5 r}{4}$