Question

Which expression is equivalent to (4g3h2k4)3

Answer 1

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

`((4g^(3) h^(2)k^(4) )^(3) )/(8g^(3)h^(2) ) - (h^(5) k^(3) )^(5)`
`= 8g^(6)h^(4) k^(12) - (h^(25) k^(15) )`

Explanation:

Explanation

Given expression

=
`((4g^(3) h^(2)k^(4) )^(3) )/(8g^(3)h^(2) ) - (h^(5) k^(3) )^(5)`

By using

(ab)ⁿ = aⁿbⁿ

`(a^(m) )/(a^(n) ) = a^(m-n)`

=
`((4)^(3) g^(9) h^(6)k^(12) ) )/(8g^(3)h^(2) ) - (h^(5) k^(3) )^(5)`

After simplification , we get

`= 8g^(9)g^(-3) h^(6) h^(-2) k^(12) - (h^(5) k^(3) )^(5)`

`= 8g^(9-3)h^(6-2) k^(12) - (h^(5) k^(3) )^(5)`

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