How do you simplify ${(2 m^{2} n)}^{2} \cdot 3 m n$ $(2m^2n)^2*3mn$ ?

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How do you simplify ${(2 m^{2} n)}^{2} \cdot 3 m n$ $(2m^2n)^2*3mn$ ?

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Answer 1 · 2018-03-26T01:40:02

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

Explanation:

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

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

2) Multiply
$(4 m^{4} n^{2}) (3 m n)$ $(4m^(4)n^2)(3mn)$
$12 m^{5} n^{3}$ $12m^5n^3$

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

Answer 2 · 2018-03-26T01:55:29

${(2 m^{2} n)}^{2} \cdot 3 m n = 12 m^{5} m^{3}$ $(2m^2n)^2*3mn=color(blue)(12m^5m^3$

Explanation:

Simplify:

${(2 m^{2} n)}^{2} \cdot 3 m n$ $(2m^2n)^2*3mn$

Apply multiplication distributive property of exponents:

${(x y)}^{a} = x^{a} y^{a}$ $(xy)^a=x^ay^a$

$2^{2} {(m^{2})}^{2} n^{2} \cdot 3 m n$ $2^2(m^2)^2n^2*3mn$

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

$4 {(m^{2})}^{2} n^{2} \cdot 3 m n$ $4(m^2)^2n^2*3mn$

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

$4 (m^{2 \cdot 2}) n^{2} \cdot 3 m n$ $4(m^(2*2))n^2*3mn$

Simplify.

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

Multiply the constants.

$4 \times 3 m^{4} n^{2} m n$ $4xx3m^4n^2mn$

Simplify.

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

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

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

Simplily.

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

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How do you simplify ${(2 m^{2} n)}^{2} \cdot 3 m n$ $(2m^2n)^2*3mn$ ?

2 Answers

Explanation:

Explanation:

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How do you simplify ${(2 m^{2} n)}^{2} \cdot 3 m n$ $(2m^2n)^2*3mn$ ?