Question

Please help it's due today. Also please don't help if you don't know.​

Answer 1

D)
`8g^(6) h^(4) k^(12) -h^(25)k^(15)`

Explanation:

You have to use the laws of exponents to solve this:

Power of a Power:
`(a^(m) )^(n) = a^(mn)`. In this case,
`(4g^(3) h^(2) k^(4) )^(3)`, all of the numbers in the parenthesis need to be multiplied to the power of 3:
`4^(3) g^(9) h^(6) k^(12)`.

Quotient of Powers:
`(a^(m) )/(a^(n) ) = a^(m-n)`. In this case,
`(4^(3) g^(9) h^(6) k^(12))/(8g^(3) h^(2) )`, all of the exponents need to be subtracted (but the 4³ (64) and 8 need to be divided):
`8g^(6) h^(4) k^(12)`.

Use the Power of a Power again for the expression at the right:
`(h^(5) k^(3) )^(5)`. You get:
`h^(25) k^(15)`. Keep the subtraction/negative sign where it is.

Together, you get:
`8g^(6) h^(4) k^(12) -h^(25)k^(15)`.

Hope it helps!