How do you simplify #(1/2k^8v^3)^2(60kv^4)#?

2 Answers
MoominDave
Jun 24, 2018

#15k^17v^10#

Explanation:

#(1/2k^8v^3)^2(60kv^4)=#
#1/4k^16v^6*60kv^4=#
#15k^17v^10#

Patrick H.
Jun 24, 2018

To get our answer, #15k^17v^10#, we can use some exponent rules for simplification.

Explanation:

Let's first simplify the left side of the expression, #(1/2k^8v^3)^2#. Notice how there is a coefficient and two variables. Each one will be squared when simplified. Let's also keep in mind that #(a^b)^c = a^(b*c)#:

#(1/2)^2=1^2/2^2=1/4#
#(k^8)^2=k^(8*2)=k^16#
#(v^3)^2=v^(3*2)=v^6#

We now have #1/4k^16v^6#. Let's multiply that by the other half of the expression. Remember that #a^b*a^c=a^(b+c)#:

#1/4*60=15#
#k^16*k=k^(16+1)=k^17#
#v^6*v^4=v^(6+4)=v^10#

We now have our final expression, #15k^17v^10#.

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