Question

Question 3 Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.

Answer 1

4x

Explanation:

Given:

√x • 4√x

Required:

Simplify in rational exponent form

SOLUTION:

Recall =>
`√(a) = a^{(1)/(2)}`

Thus,

`√(x)*4√(x)` can be expressed in exponent form as
`x^{(1)/(2)}*4x^{(1)/(2)`

When multiplying 2 bases having exponents together, their exponents should be added together, while you multiply the bases. I.e.
`x^m*x^n = x^(m+n )`

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

`= 4x^(1) = 4x`

The answer is 4x