Simplify ((5pr^-2)^-2)/((3p^-1r)^3)

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

Move ${(5 p r^{- 2})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Simplify the denominator.

Apply the product rule to $3 p^{- 1} r$ .

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

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

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

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

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

Combine $3$ and $\frac{1}{p}$ .

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

Apply the product rule to $\frac{3}{p}$ .

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

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

$\frac{1}{\frac{27}{p^{3}} r^{3} {(5 p)}^{2} {(r^{- 2})}^{2}}$

Apply the product rule to $5 p$ .

$\frac{1}{\frac{27}{p^{3}} r^{3} (5^{2} p^{2}) {(r^{- 2})}^{2}}$

Raise $5$ to the power of $2$ .

$\frac{1}{\frac{27}{p^{3}} r^{3} (25 p^{2}) {(r^{- 2})}^{2}}$

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

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

$\frac{1}{\frac{27}{p^{3}} r^{3} (25 p^{2}) r^{- 2 \cdot 2}}$

Multiply $- 2$ by $2$ .

$\frac{1}{\frac{27}{p^{3}} r^{3} (25 p^{2}) r^{- 4}}$

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

$\frac{1}{\frac{27}{p^{3}} r^{3} \cdot 25 p^{2} \frac{1}{r^{4}}}$

Combine exponents.

Combine $\frac{27}{p^{3}}$ and $r^{3}$ .

$\frac{1}{\frac{27 r^{3}}{p^{3}} \cdot 25 p^{2} \frac{1}{r^{4}}}$

Combine $\frac{27 r^{3}}{p^{3}}$ and $25$ .

$\frac{1}{\frac{27 r^{3} \cdot 25}{p^{3}} p^{2} \frac{1}{r^{4}}}$

Multiply $25$ by $27$ .

$\frac{1}{\frac{675 r^{3}}{p^{3}} p^{2} \frac{1}{r^{4}}}$

Combine $\frac{675 r^{3}}{p^{3}}$ and $p^{2}$ .

$\frac{1}{\frac{675 r^{3} p^{2}}{p^{3}} \cdot \frac{1}{r^{4}}}$

Multiply $\frac{675 r^{3} p^{2}}{p^{3}}$ by $\frac{1}{r^{4}}$ .

$\frac{1}{\frac{675 r^{3} p^{2}}{p^{3} r^{4}}}$

Reduce the expression $\frac{675 r^{3} p^{2}}{p^{3} r^{4}}$ by cancelling the common factors.

Factor $r^{3}$ out of $675 r^{3} p^{2}$ .

$\frac{1}{\frac{r^{3} (675 p^{2})}{p^{3} r^{4}}}$

Factor $r^{3}$ out of $p^{3} r^{4}$ .

$\frac{1}{\frac{r^{3} (675 p^{2})}{r^{3} (p^{3} r)}}$

Cancel the common factor.

$\frac{1}{\frac{r^{3} (675 p^{2})}{r^{3} (p^{3} r)}}$

Rewrite the expression.

$\frac{1}{\frac{675 p^{2}}{p^{3} r}}$

Cancel the common factor of $p^{2}$ and $p^{3}$ .

Factor $p^{2}$ out of $675 p^{2}$ .

$\frac{1}{\frac{p^{2} \cdot 675}{p^{3} r}}$

Cancel the common factors.

Factor $p^{2}$ out of $p^{3} r$ .

$\frac{1}{\frac{p^{2} \cdot 675}{p^{2} (p r)}}$

Cancel the common factor.

$\frac{1}{\frac{p^{2} \cdot 675}{p^{2} (p r)}}$

Rewrite the expression.

$\frac{1}{\frac{675}{p r}}$

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{p r}{675}$

Multiply $\frac{p r}{675}$ by $1$ .

$\frac{p r}{675}$

Simplify ((5pr^-2)^-2)/((3p^-1r)^3)

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