Simplify ((-5p^-2)^3)/(-4p^-1)

$\frac{{(- 5 p^{- 2})}^{3}}{- 4 p^{- 1}}$

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

$\frac{{(- 5 p^{- 2})}^{3} p}{- 4}$

Simplify the numerator.

Apply the product rule to $- 5 p^{- 2}$ .

$\frac{{(- 5)}^{3} {(p^{- 2})}^{3} p}{- 4}$

Raise $- 5$ to the power of $3$ .

$\frac{- 125 {(p^{- 2})}^{3} p}{- 4}$

Multiply the exponents in ${(p^{- 2})}^{3}$ .

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

$\frac{- 125 p^{- 2 \cdot 3} p}{- 4}$

Multiply $- 2$ by $3$ .

$\frac{- 125 p^{- 6} p}{- 4}$

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

$\frac{- 125 \frac{1}{p^{6}} p}{- 4}$

Combine exponents.

Combine $- 125$ and $\frac{1}{p^{6}}$ .

$\frac{\frac{- 125}{p^{6}} p}{- 4}$

Combine $\frac{- 125}{p^{6}}$ and $p$ .

$\frac{\frac{- 125 p}{p^{6}}}{- 4}$

Reduce the expression $\frac{- 125 p}{p^{6}}$ by cancelling the common factors.

Factor $p$ out of $- 125 p$ .

$\frac{\frac{p \cdot - 125}{p^{6}}}{- 4}$

Factor $p$ out of $p^{6}$ .

$\frac{\frac{p \cdot - 125}{p \cdot p^{5}}}{- 4}$

Cancel the common factor.

$\frac{\frac{p \cdot - 125}{p \cdot p^{5}}}{- 4}$

Rewrite the expression.

$\frac{\frac{- 125}{p^{5}}}{- 4}$

Move the negative in front of the fraction.

$\frac{- \frac{125}{p^{5}}}{- 4}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{125}{p^{5}} \cdot \frac{1}{- 4}$

Move the negative in front of the fraction.

$- \frac{125}{p^{5}} (- \frac{1}{4})$

Multiply $- \frac{125}{p^{5}} (- \frac{1}{4})$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{125}{p^{5}} \frac{1}{4}$

Multiply $\frac{125}{p^{5}}$ by $1$ .

$\frac{125}{p^{5}} \cdot \frac{1}{4}$

Multiply $\frac{125}{p^{5}}$ by $\frac{1}{4}$ .

$\frac{125}{p^{5} \cdot 4}$

Move $4$ to the left of $p^{5}$ .

$\frac{125}{4 p^{5}}$