# How do you simplify (2m^2n)^2*3mn?

Mar 26, 2018

$12 {m}^{5} {n}^{3}$

#### Explanation:

1) Distribute the exponent of 2 so that:
${2}^{2} {m}^{2 \left(2\right)} {n}^{2}$

*Remember: when applying an exponent to another exponent, multiply the exponents

2) Multiply
$\left(4 {m}^{4} {n}^{2}\right) \left(3 m n\right)$
$12 {m}^{5} {n}^{3}$

*Remember: when multiplying two variables with the same base, add the exponents

Mar 26, 2018

(2m^2n)^2*3mn=color(blue)(12m^5m^3

#### Explanation:

Simplify:

${\left(2 {m}^{2} n\right)}^{2} \cdot 3 m n$

Apply multiplication distributive property of exponents:

${\left(x y\right)}^{a} = {x}^{a} {y}^{a}$

${2}^{2} {\left({m}^{2}\right)}^{2} {n}^{2} \cdot 3 m n$

Simplify ${2}^{2}$ to $4$.

$4 {\left({m}^{2}\right)}^{2} {n}^{2} \cdot 3 m n$

Apply power rule of exponents: ${\left({x}^{a}\right)}^{b} = {a}^{a \cdot b}$

$4 \left({m}^{2 \cdot 2}\right) {n}^{2} \cdot 3 m n$

Simplify.

$4 {m}^{4} {n}^{2} \cdot 3 m n$

Multiply the constants.

$4 \times 3 {m}^{4} {n}^{2} m n$

Simplify.

$12 {m}^{4} {n}^{2} m n$

Apply product rule of exponents: ${x}^{a} {x}^{b} = {x}^{a + b}$

$12 {m}^{4 + 1} {n}^{2 + 1}$

Simplily.

$12 {m}^{5} {m}^{3}$