Question

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

Answer 1

`12m^5n^3`

Explanation:

1) Distribute the exponent of 2 so that:
`2^2m^(2(2))n^2`

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

2) Multiply
`(4m^(4)n^2)(3mn)`
`12m^5n^3`

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

Answer 2

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

Explanation:

Simplify:

`(2m^2n)^2*3mn`

Apply multiplication distributive property of exponents:

`(xy)^a=x^ay^a`

`2^2(m^2)^2n^2*3mn`

Simplify `2^2` to `4`.

`4(m^2)^2n^2*3mn`

Apply power rule of exponents: `(x^a)^b=a^(a*b)`

`4(m^(2*2))n^2*3mn`

Simplify.

`4m^4n^2*3mn`

Multiply the constants.

`4xx3m^4n^2mn`

Simplify.

`12m^4n^2mn`

Apply product rule of exponents: `x^ax^b=x^(a+b)`

`12m^(4+1)n^(2+1)`

Simplily.

`12m^5m^3`