Question

3. Simplify.

312⋅312

4. Rewrite n√xm

using a rational expression.

Answer 1

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

`\sqrt[n]{x^m}=x^{(m)/(n)}`

Explanation:

We have been given a radical expression
`3^{(1)/(2)}\cdot 3^{(1)/(2)}`. We are asked to simplify our given expression.

Using exponent property
`a^b\cdot a^c=a^(b+c)`, we can rewrite our given expression as:

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

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

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

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

Therefore, the simplified form of our given expression would be 3.

Using exponent property for radical
`\sqrt[n]{a^m}=a^{(m)/(n)}`, we can rewrite our given expression as:

`\sqrt[n]{x^m}=x^{(m)/(n)}`

Therefore, after writing our given expression as a rational expression we will get
`x^{(m)/(n)}`.

Answer 2

Explanation:

Left

As near as I can tell, the question is x^(1/2) * x^(1/2) = The bases are the same, so all you do is add the powers.

x^(1/2 + 1/2) = x^1 which is just x.

Right

The is another one where the work is hard to show. The numerator (m) of the fraction is the power and the denominator (n) is the root. That sentence is all the work there is.

So you would write
`\sqrt[m]{x^(n) } = x^{(m)/(n) }`