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

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Answer 1 · 2018-03-26T01:40:02

#12m^5n^3#

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 · 2018-03-26T01:55:29

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

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#