Question

Simplify the expression (3 1/4)^2 to demonstrate the power of a power property. Show any intermittent steps that demonstrate how you arrived at the simplified answer. 30 points

Answer 1

By property of power of a power:

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

Explanation:

Given that
`(3^{(1)/(4)} )^(2)`

The property of power of a power is given by,

=
`(a^(b) )^(2)`

=
`(a^(b) )* (a^(b) )`

=
`(a^((b+b)) )`

Using the property of power of a power:

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

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

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

=
`3^{((1)/(2))}`