Simplify (-4a^3b^2)^2*(3a^2b)

${(- 4 a^{3} b^{2})}^{2} \cdot (3 a^{2} b)$

Step 1

Rewrite using the commutative property of multiplication.

$3 {(- 4 a^{3} b^{2})}^{2} a^{2} b$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- 4 a^{3} b^{2}$ .

$3 ({(- 4 a^{3})}^{2} {(b^{2})}^{2}) a^{2} b$

Apply the product rule to $- 4 a^{3}$ .

$3 ({(- 4)}^{2} {(a^{3})}^{2} {(b^{2})}^{2}) a^{2} b$

Step 3

Raise $- 4$ to the power of $2$ .

$3 (16 {(a^{3})}^{2} {(b^{2})}^{2}) a^{2} b$

Step 4

Multiply the exponents in ${(a^{3})}^{2}$ .

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

$3 (16 a^{3 \cdot 2} {(b^{2})}^{2}) a^{2} b$

Multiply $3$ by $2$ .

$3 (16 a^{6} {(b^{2})}^{2}) a^{2} b$

Step 5

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

Move $a^{2}$ .

$3 (16 (a^{2} a^{6}) {(b^{2})}^{2}) b$

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

$3 (16 a^{2 + 6} {(b^{2})}^{2}) b$

Add $2$ and $6$ .

$3 (16 a^{8} {(b^{2})}^{2}) b$

Step 6

Multiply the exponents in ${(b^{2})}^{2}$ .

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

$3 (16 a^{8} b^{2 \cdot 2}) b$

Multiply $2$ by $2$ .

$3 (16 a^{8} b^{4}) b$

Step 7

Multiply $b^{4}$ by $b$ by adding the exponents.

Move $b$ .

$3 (16 a^{8} (b \cdot b^{4}))$

Multiply $b$ by $b^{4}$ .

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

$3 (16 a^{8} (b^{1} b^{4}))$

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

$3 (16 a^{8} b^{1 + 4})$

Add $1$ and $4$ .

$3 (16 a^{8} b^{5})$

Step 8

Multiply $16$ by $3$ .

$48 a^{8} b^{5}$

Simplify (-4a^3b^2)^2*(3a^2b)

Related Questions

Support LCMGCF.com by disabling your adblocker.