Rewrite in simplest rational exponent form square root of x times the fourth root of x.

Question

Show each step of your process.

Answer 1

The square root of x can be written as x^1/2 in exponential form.

The fourth root of x can be written as x^1/4.

x^1/2 * x^1/4 = x^1/2+1/4 = x^2/4+1/4 = x^3/4

We use exponent rules. When multiplying two numbers with same base, you add the exponents.

To add 1/2 and 1/4 you need a common denominator (1/2 is equivalent to 2/4).

Then add and you're done! :)

Answer 2

the square root of X can be written in exponential like X^1/2

and the fourth root of X in exponential form is X^1/4

so the problem can be rewritten in exponential and solved like below:

X^1/2 x X^1/4 =

X^{(1/2 + 1/4)} =

X^{(2/4 + 1/4)} =

X^3/4