Question

What is this in simplest rational exponent form

Answer 1

`4x`

Explanation:

We want to find the simplest rational exponent form of

`√(x) \cdot 4√(x)`

Recall that:
`√(a)=a^{(1)/(2) }`

We rewrite the expression in the exponent form to get:

`x^{(1)/(2)}\cdot 4x^{(1)/(2)`

We can regroup the product to get:

`4 x^{(1)/(2)\cdot x^{(1)/(2)`

We apply the rule:
`a^m\cdot a^n=a6{m+n}` to get:

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

`4 x^{(1)/(2)}\cdot x^{(1)/(2)=4 x^(1)`

`4 x^{(1)/(2)}\cdot x^{(1)/(2)=4x`