Question

Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form.

(2•6)3/2​

Answer 1

`(2\cdot 6)^{(3)/(2)}=24(3)^{(1)/(2)}`

Explanation:

The given expression is
`(2*6)^{(3)/(2)}`

We multiply within the parenthesis to get:

`(12)^{(3)/(2)}`

Recall that:
`a^{(m)/(n) } =\sqrt[n]{x^m}`

We apply this property to get:

`(12)^{(3)/(2)}=√(12^3)`

`(12)^{(3)/(2)}=√(12^2*12)`

This simplifies to

`(12)^{(3)/(2)}=12√(12)`

We can simplify further

`(12)^{(3)/(2)}=12√(4*3)=12*2√(3)=24√(3)`

We rewrite as rational exponent
`24(3)^{(1)/(2)}`