Simplify (3a^0b^2)(2a^3b^2)^2

$(3 a^{0} b^{2}) {(2 a^{3} b^{2})}^{2}$

Step 1

Anything raised to $0$ is $1$ .

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

Step 2

Multiply $3$ by $1$ .

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

Step 3

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

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

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

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

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

Step 4

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

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

Step 5

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

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

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

Multiply $3$ by $2$ .

$3 b^{2} (4 a^{6} {(b^{2})}^{2})$

Step 6

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

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

$3 b^{2} (4 a^{6} b^{2 \cdot 2})$

Multiply $2$ by $2$ .

$3 b^{2} (4 a^{6} b^{4})$

Step 7

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

Move $b^{4}$ .

$3 (b^{4} b^{2}) (4 a^{6})$

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

$3 b^{4 + 2} (4 a^{6})$

Add $4$ and $2$ .

$3 b^{6} (4 a^{6})$

Step 8

Rewrite using the commutative property of multiplication.

$3 \cdot 4 b^{6} a^{6}$

Step 9

Multiply $3$ by $4$ .

$12 b^{6} a^{6}$