Simplify -3a^2b*7(a^9)^5

$- 3 a^{2} b \cdot 7 {(a^{9})}^{5}$

Step 1

Multiply the exponents in ${(a^{9})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 3 a^{2} b \cdot (7 a^{9 \cdot 5})$

Multiply $9$ by $5$ .

$- 3 a^{2} b \cdot (7 a^{45})$

Step 2

Multiply $a^{2}$ by $a^{45}$ by adding the exponents.

Move $a^{45}$ .

$- 3 (a^{45} a^{2}) b \cdot 7$

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

$- 3 a^{45 + 2} b \cdot 7$

Add $45$ and $2$ .

$- 3 a^{47} b \cdot 7$

Step 3

Multiply $7$ by $- 3$ .

$- 21 a^{47} b$