# How do you simplify (3a ^ { 2} b ) ^ { 2} ( 2a ^ { 3} b ^ { 4} )?

Oct 9, 2017

(3a^2b)^2(2a^3b^4)=color(blue)(18a^7b^6

Refer to the explanation for the process.

#### Explanation:

Simplify:

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

Apply the exponent power rule: ${\left({x}^{m}\right)}^{n} = {x}^{m \cdot n}$.
(No exponent is understood to be $1$.)

$\left({3}^{1 \cdot 2} {a}^{2 \cdot 2} {b}^{1 \cdot 2}\right) \left(2 {a}^{3} {b}^{4}\right)$

Simplify.

$\left({3}^{2} {a}^{4} {b}^{2}\right) \left(2 {a}^{3} {b}^{4}\right) =$

$\left(9 {a}^{4} {b}^{2}\right) \left(2 {a}^{3} {b}^{4}\right)$

Gather like terms.

$\left(9 \times 2\right) \left({a}^{4} {a}^{3}\right) \left({b}^{2} {b}^{4}\right)$

Apply the exponent product rule: ${x}^{m} {x}^{n} = {x}^{m + n}$.

$9 \times 2 {a}^{4 + 3} {b}^{2 + 4}$

Simplify.

$18 {a}^{7} {b}^{6}$