Simplify (25a^-5b^-8)/(5a^4b)

$\frac{25 a^{- 5} b^{- 8}}{5 a^{4} b}$

Step 1

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

$\frac{25 b^{- 8}}{5 a^{4} b a^{5}}$

Step 2

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

$\frac{25}{5 a^{4} b a^{5} b^{8}}$

Step 3

Simplify the denominator.

Multiply $a^{4}$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$\frac{25}{5 (a^{5} a^{4}) b \cdot b^{8}}$

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

$\frac{25}{5 a^{5 + 4} b \cdot b^{8}}$

Add $5$ and $4$ .

$\frac{25}{5 a^{9} b \cdot b^{8}}$

Multiply $b$ by $b^{8}$ by adding the exponents.

Move $b^{8}$ .

$\frac{25}{5 a^{9} (b^{8} b)}$

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

Raise $b$ to the power of $1$ .

$\frac{25}{5 a^{9} (b^{8} b^{1})}$

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

$\frac{25}{5 a^{9} b^{8 + 1}}$

Add $8$ and $1$ .

$\frac{25}{5 a^{9} b^{9}}$

Step 4

Cancel the common factor of $25$ and $5$ .

Factor $5$ out of $25$ .

$\frac{5 \cdot 5}{5 a^{9} b^{9}}$

Cancel the common factors.

Factor $5$ out of $5 a^{9} b^{9}$ .

$\frac{5 \cdot 5}{5 (a^{9} b^{9})}$

Cancel the common factor.

$\frac{5 \cdot 5}{5 (a^{9} b^{9})}$

Rewrite the expression.

$\frac{5}{a^{9} b^{9}}$