Write the Fraction in Simplest Form (-5d^-3)/(-4(d^-5)^3)

$\frac{- 5 d^{- 3}}{- 4 {(d^{- 5})}^{3}}$

Step 1

Move $d^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 5}{- 4 {(d^{- 5})}^{3} d^{3}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(d^{- 5})}^{3}$ .

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

$\frac{- 5}{- 4 d^{- 5 \cdot 3} d^{3}}$

Multiply $- 5$ by $3$ .

$\frac{- 5}{- 4 d^{- 15} d^{3}}$

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

$\frac{- 5}{- 4 \frac{1}{d^{15}} d^{3}}$

Combine exponents.

Combine $- 4$ and $\frac{1}{d^{15}}$ .

$\frac{- 5}{\frac{- 4}{d^{15}} d^{3}}$

Combine $\frac{- 4}{d^{15}}$ and $d^{3}$ .

$\frac{- 5}{\frac{- 4 d^{3}}{d^{15}}}$

Reduce the expression $\frac{- 4 d^{3}}{d^{15}}$ by cancelling the common factors.

Factor $d^{3}$ out of $- 4 d^{3}$ .

$\frac{- 5}{\frac{d^{3} \cdot - 4}{d^{15}}}$

Factor $d^{3}$ out of $d^{15}$ .

$\frac{- 5}{\frac{d^{3} \cdot - 4}{d^{3} d^{12}}}$

Cancel the common factor.

$\frac{- 5}{\frac{d^{3} \cdot - 4}{d^{3} d^{12}}}$

Rewrite the expression.

$\frac{- 5}{\frac{- 4}{d^{12}}}$

Move the negative in front of the fraction.

$\frac{- 5}{- \frac{4}{d^{12}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- 5 (- \frac{d^{12}}{4})$

Step 4

Multiply $- 5 (- \frac{d^{12}}{4})$ .

Multiply $- 1$ by $- 5$ .

$5 \frac{d^{12}}{4}$

Combine $5$ and $\frac{d^{12}}{4}$ .

$\frac{5 d^{12}}{4}$