Simplify (20b^-8r^-9)/((5b^4r^-5)^-2)

$\frac{20 b^{- 8} r^{- 9}}{{(5 b^{4} r^{- 5})}^{- 2}}$

Simplify.

Move $b^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{20 r^{- 9}}{{(5 b^{4} r^{- 5})}^{- 2} b^{8}}$

Move $r^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{20}{{(5 b^{4} r^{- 5})}^{- 2} b^{8} r^{9}}$

Move ${(5 b^{4} r^{- 5})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{20 {(5 b^{4} r^{- 5})}^{2}}{b^{8} r^{9}}$

Simplify the numerator.

Apply the product rule to $5 b^{4} r^{- 5}$ .

$\frac{20 {(5 b^{4})}^{2} {(r^{- 5})}^{2}}{b^{8} r^{9}}$

Apply the product rule to $5 b^{4}$ .

$\frac{20 (5^{2} {(b^{4})}^{2}) {(r^{- 5})}^{2}}{b^{8} r^{9}}$

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

$\frac{20 (25 {(b^{4})}^{2}) {(r^{- 5})}^{2}}{b^{8} r^{9}}$

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

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

$\frac{20 (25 b^{4 \cdot 2}) {(r^{- 5})}^{2}}{b^{8} r^{9}}$

Multiply $4$ by $2$ .

$\frac{20 (25 b^{8}) {(r^{- 5})}^{2}}{b^{8} r^{9}}$

Multiply the exponents in ${(r^{- 5})}^{2}$ .

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

$\frac{20 (25 b^{8}) r^{- 5 \cdot 2}}{b^{8} r^{9}}$

Multiply $- 5$ by $2$ .

$\frac{20 (25 b^{8}) r^{- 10}}{b^{8} r^{9}}$

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

$\frac{20 \cdot 25 b^{8} \frac{1}{r^{10}}}{b^{8} r^{9}}$

Combine exponents.

Multiply $20$ by $25$ .

$\frac{500 b^{8} \frac{1}{r^{10}}}{b^{8} r^{9}}$

Combine $500$ and $\frac{1}{r^{10}}$ .

$\frac{b^{8} \frac{500}{r^{10}}}{b^{8} r^{9}}$

Combine $b^{8}$ and $\frac{500}{r^{10}}$ .

$\frac{\frac{b^{8} \cdot 500}{r^{10}}}{b^{8} r^{9}}$

Move $500$ to the left of $b^{8}$ .

$\frac{\frac{500 b^{8}}{r^{10}}}{b^{8} r^{9}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{500 b^{8}}{r^{10}} \cdot \frac{1}{b^{8} r^{9}}$

Combine.

$\frac{500 b^{8} \cdot 1}{r^{10} (b^{8} r^{9})}$

Multiply $r^{10}$ by $r^{9}$ by adding the exponents.

Move $r^{9}$ .

$\frac{500 b^{8} \cdot 1}{r^{9} r^{10} b^{8}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{500 b^{8} \cdot 1}{r^{9 + 10} b^{8}}$

Add $9$ and $10$ .

$\frac{500 b^{8} \cdot 1}{r^{19} b^{8}}$

Multiply $500 b^{8}$ by $1$ .

$\frac{500 b^{8}}{r^{19} b^{8}}$

Cancel the common factor of $b^{8}$ .

Cancel the common factor.

$\frac{500 b^{8}}{r^{19} b^{8}}$

Rewrite the expression.

$\frac{500}{r^{19}}$

Simplify (20b^-8r^-9)/((5b^4r^-5)^-2)

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