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

2 Answers
Jun 24, 2018

15k^17v^10

Explanation:

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

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.