Simplify 7a^4b^-5*2a^2b

$7 a^{4} b^{- 5} \cdot 2 a^{2} b$

Step 1

Multiply $a^{4}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$7 (a^{2} a^{4}) b^{- 5} \cdot (2 b)$

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

$7 a^{2 + 4} b^{- 5} \cdot (2 b)$

Add $2$ and $4$ .

$7 a^{6} b^{- 5} \cdot (2 b)$

Step 2

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

Move $b$ .

$7 a^{6} (b \cdot b^{- 5}) \cdot 2$

Multiply $b$ by $b^{- 5}$ .

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

$7 a^{6} (b^{1} b^{- 5}) \cdot 2$

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

$7 a^{6} b^{1 - 5} \cdot 2$

Subtract $5$ from $1$ .

$7 a^{6} b^{- 4} \cdot 2$

Step 3

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

$7 a^{6} \frac{1}{b^{4}} \cdot 2$

Step 4

Multiply $7 a^{6} \frac{1}{b^{4}}$ .

Combine $7$ and $\frac{1}{b^{4}}$ .

$a^{6} \frac{7}{b^{4}} \cdot 2$

Combine $a^{6}$ and $\frac{7}{b^{4}}$ .

$\frac{a^{6} \cdot 7}{b^{4}} \cdot 2$

Step 5

Move $7$ to the left of $a^{6}$ .

$\frac{7 \cdot a^{6}}{b^{4}} \cdot 2$

Step 6

Multiply $\frac{7 a^{6}}{b^{4}} \cdot 2$ .

Combine $\frac{7 a^{6}}{b^{4}}$ and $2$ .

$\frac{7 a^{6} \cdot 2}{b^{4}}$

Multiply $2$ by $7$ .

$\frac{14 a^{6}}{b^{4}}$