Simplify 2a^2b^-3*5ab

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

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

Move $a$ .

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

Multiply $a$ by $a^{2}$ .

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

$2 (a^{1} a^{2}) b^{- 3} \cdot (5 b)$

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

$2 a^{1 + 2} b^{- 3} \cdot (5 b)$

Add $1$ and $2$ .

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

Multiply $b^{- 3}$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b^{- 3}$ .

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

$2 a^{3} (b^{1} b^{- 3}) \cdot 5$

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

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

Subtract $3$ from $1$ .

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

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

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

Multiply $2 a^{3} \frac{1}{b^{2}}$ .

Combine $2$ and $\frac{1}{b^{2}}$ .

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

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

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

Move $2$ to the left of $a^{3}$ .

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

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

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

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

Multiply $5$ by $2$ .

$\frac{10 a^{3}}{b^{2}}$