Simplify (10a^-8b^-2)/(4a^3b^5)

$\frac{10 a^{- 8} b^{- 2}}{4 a^{3} b^{5}}$

Step 1

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

$\frac{10 b^{- 2}}{4 a^{3} b^{5} a^{8}}$

Step 2

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

$\frac{10}{4 a^{3} b^{5} a^{8} b^{2}}$

Step 3

Simplify the denominator.

Multiply $a^{3}$ by $a^{8}$ by adding the exponents.

Move $a^{8}$ .

$\frac{10}{4 (a^{8} a^{3}) b^{5} b^{2}}$

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

$\frac{10}{4 a^{8 + 3} b^{5} b^{2}}$

Add $8$ and $3$ .

$\frac{10}{4 a^{11} b^{5} b^{2}}$

Multiply $b^{5}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$\frac{10}{4 a^{11} (b^{2} b^{5})}$

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

$\frac{10}{4 a^{11} b^{2 + 5}}$

Add $2$ and $5$ .

$\frac{10}{4 a^{11} b^{7}}$

Step 4

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$\frac{2 (5)}{4 a^{11} b^{7}}$

Cancel the common factors.

Factor $2$ out of $4 a^{11} b^{7}$ .

$\frac{2 (5)}{2 (2 a^{11} b^{7})}$

Cancel the common factor.

$\frac{2 \cdot 5}{2 (2 a^{11} b^{7})}$

Rewrite the expression.

$\frac{5}{2 a^{11} b^{7}}$