Write the Fraction in Simplest Form (20a^-5w^-8)/(-5(a^-5w^-1)^-4)

$\frac{20 a^{- 5} w^{- 8}}{- 5 {(a^{- 5} w^{- 1})}^{- 4}}$

Move $a^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{20 w^{- 8}}{- 5 {(a^{- 5} w^{- 1})}^{- 4} a^{5}}$

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

$\frac{20}{- 5 {(a^{- 5} w^{- 1})}^{- 4} a^{5} w^{8}}$

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

$\frac{20 {(a^{- 5} w^{- 1})}^{4}}{- 5 a^{5} w^{8}}$

Cancel the common factor of $20$ and $- 5$ .

Factor $5$ out of $20 {(a^{- 5} w^{- 1})}^{4}$ .

$\frac{5 (4 {(a^{- 5} w^{- 1})}^{4})}{- 5 a^{5} w^{8}}$

Cancel the common factors.

Factor $5$ out of $- 5 a^{5} w^{8}$ .

$\frac{5 (4 {(a^{- 5} w^{- 1})}^{4})}{5 (- a^{5} w^{8})}$

Cancel the common factor.

$\frac{5 (4 {(a^{- 5} w^{- 1})}^{4})}{5 (- a^{5} w^{8})}$

Rewrite the expression.

$\frac{4 {(a^{- 5} w^{- 1})}^{4}}{- a^{5} w^{8}}$

Simplify the numerator.

Apply the product rule to $a^{- 5} w^{- 1}$ .

$\frac{4 {(a^{- 5})}^{4} {(w^{- 1})}^{4}}{- a^{5} w^{8}}$

Multiply the exponents in ${(a^{- 5})}^{4}$ .

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

$\frac{4 a^{- 5 \cdot 4} {(w^{- 1})}^{4}}{- a^{5} w^{8}}$

Multiply $- 5$ by $4$ .

$\frac{4 a^{- 20} {(w^{- 1})}^{4}}{- a^{5} w^{8}}$

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

$\frac{4 \frac{1}{a^{20}} {(w^{- 1})}^{4}}{- a^{5} w^{8}}$

Multiply the exponents in ${(w^{- 1})}^{4}$ .

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

$\frac{4 \frac{1}{a^{20}} w^{- 1 \cdot 4}}{- a^{5} w^{8}}$

Multiply $- 1$ by $4$ .

$\frac{4 \frac{1}{a^{20}} w^{- 4}}{- a^{5} w^{8}}$

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

$\frac{4 \frac{1}{a^{20}} \frac{1}{w^{4}}}{- a^{5} w^{8}}$

Combine exponents.

Combine $4$ and $\frac{1}{a^{20}}$ .

$\frac{\frac{4}{a^{20}} \cdot \frac{1}{w^{4}}}{- a^{5} w^{8}}$

Multiply $\frac{4}{a^{20}}$ by $\frac{1}{w^{4}}$ .

$\frac{\frac{4}{a^{20} w^{4}}}{- a^{5} w^{8}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{a^{20} w^{4}} \cdot \frac{1}{- a^{5} w^{8}}$

Combine.

$\frac{4 \cdot 1}{a^{20} w^{4} (- a^{5} w^{8})}$

Multiply $a^{20}$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$\frac{4 \cdot 1}{a^{5} a^{20} w^{4} (- w^{8})}$

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

$\frac{4 \cdot 1}{a^{5 + 20} w^{4} (- w^{8})}$

Add $5$ and $20$ .

$\frac{4 \cdot 1}{a^{25} w^{4} (- w^{8})}$

Multiply $w^{4}$ by $w^{8}$ by adding the exponents.

Move $w^{8}$ .

$\frac{4 \cdot 1}{a^{25} (w^{8} w^{4}) \cdot - 1}$

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

$\frac{4 \cdot 1}{a^{25} w^{8 + 4} \cdot - 1}$

Add $8$ and $4$ .

$\frac{4 \cdot 1}{a^{25} w^{12} \cdot - 1}$

Multiply $4$ by $1$ .

$\frac{4}{a^{25} w^{12} \cdot - 1}$

Move $- 1$ to the left of $a^{25} w^{12}$ .

$\frac{4}{- 1 \cdot (a^{25} w^{12})}$

Move the negative in front of the fraction.

$- \frac{4}{a^{25} w^{12}}$

Write the Fraction in Simplest Form (20a^-5w^-8)/(-5(a^-5w^-1)^-4)

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