Question

3^4 × h^5 × g^2 / 3^2 × h^8

Could you show me the steps so I can understand easier?

Answer 1

`(3^(2) * g^(2))/(h^(3) )`

Explanation:

We have to simplify the following mathematical expression.

The expression is
`(3^(4) * h^(5) * g^(2))/(3^(2) * h^(8)   )`

Now,
`(3^(4) * h^(5) * g^(2))/(3^(2) * h^(8)   )`

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

{Since, all the terms are in product form, so, we can treat them separately}

{We know the formula of exponent
`(x^(a) )/(x^(b) )  = x^((a - b))`}

=
`3^(2) * h^(- 3) * g^(2)`

=
`(3^(2) * g^(2))/(h^(3) )` (Answer)

{Since, we know,
`x^(- a) = (1)/(x^(a))`}