Question

`(3h^{(5)/(2) })( 2k^{(3)/(4) })(3h^{(5)/(2) }) (2k^{(3)/(4) })`

Please Show Your Work

Answer 1

`486h^(5)k√(2k)`

Explanation:

We have to simplify the expression
`(3h^{(5)/(2)})(2k^{(3)/(4)})(3h^{(5)/(2)})(2k^{(3)/(4)})`

Now,

`(3h^{(5)/(2)})(2k^{(3)/(4)})(3h^{(5)/(2)})(2k^{(3)/(4)})`

=
`(3^{(5)/(2)}* 3^{(5)/(2)})* (2^{(3)/(4)} * 2^{(3)/(4)}) * (h^{(5)/(2)}* h^{(5)/(2)})* (k^{(3)/(4)} * k^{(3)/(4)})`

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

=
`3^{((5)/(2) + (5)/(2))} * 2^{((3)/(4) + (3)/(4))} * h^{((5)/(2) + (5)/(2))} * k^{((3)/(4) + (3)/(4))}`

{Since, we know that
`a^(b) * a^(c) = a^(b + c)`}

=
`3^(5) * 2^{(3)/(2)} * h^(5) * k^{(3)/(2)}`

=
`243 * 2√(2) * h^(5)* k^{(3)/(2) }`

=
`486√(2) * h^(5) * k√(k)`

=
`486h^(5)k√(2k)` (Answer)