Simplify 2a^-5b^6*5a^2b^2

$2 a^{- 5} b^{6} \cdot 5 a^{2} b^{2}$

Step 1

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

Move $a^{2}$ .

$2 (a^{2} a^{- 5}) b^{6} \cdot (5 b^{2})$

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

$2 a^{2 - 5} b^{6} \cdot (5 b^{2})$

Subtract $5$ from $2$ .

$2 a^{- 3} b^{6} \cdot (5 b^{2})$

Step 2

Multiply $b^{6}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$2 a^{- 3} (b^{2} b^{6}) \cdot 5$

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

$2 a^{- 3} b^{2 + 6} \cdot 5$

Add $2$ and $6$ .

$2 a^{- 3} b^{8} \cdot 5$

Step 3

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

$2 \frac{1}{a^{3}} b^{8} \cdot 5$

Step 4

Combine $2$ and $\frac{1}{a^{3}}$ .

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

Step 5

Combine $\frac{2}{a^{3}}$ and $b^{8}$ .

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

Step 6

Multiply $\frac{2 b^{8}}{a^{3}} \cdot 5$ .

Combine $\frac{2 b^{8}}{a^{3}}$ and $5$ .

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

Multiply $5$ by $2$ .

$\frac{10 b^{8}}{a^{3}}$