Question

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

Answer 1

`15k^17v^10`

Explanation:

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

Answer 2

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`.