Question

I don't know how to "Simplify the expression of (3 ^1\4) * (3^2) " specifically to demonstrate the product of powers property (and show any steps I used too)

Answer 1

11.85

Explanation:

(3^1\4) =
`3^{(1)/(4) }`

(3^2) =
`(3)^(2)`

Applying the law of indices,

`a^(m)` x
`a^(n)` =
`a^((m+n))`

`3^{(1)/(4) }` x
`3^(2)` =
`3^{(1)/(4) + 2}`

=
`3^{(9)/(4) }`

=
`\sqrt[4]{3^(9) }`

=
`\sqrt[4]{19683}`

= 11.8445

≅ 11.84