Question

Rewrite in simplest rational exponent form x^1/2*X^1/4

Answer 1

Answer:

x ^ (3/4)

Step-by-step explanation:

x^1/2*X^1/4

When we multiply and the bases are the same we can add the exponents

x ^ ( 1/2 + 1/4)

x ^ ( 2/4 + 1/4)

x ^ (3/4)

Answer 2

Answer:

$\sqrt[4]{x^3}$

Step-by-step explanation:

First, let's examine our original statement.

$x^{\frac{1}{2} }\cdot x^{\frac{1}{4}}$

Using exponent rules, we know that if we have $x^a \cdot x^b$, then simplified, the answer will be equivalent to $x^{a+b}$.

So we can simplify this by adding the exponents $\frac{1}{2}$ and $\frac{1}{4}$.

Converting  $\frac{1}{2}$ into fourths gets us $\frac{2}{4}$.

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.

So we now have $x^{\frac{3}{4}}$.

When we have a number to a fraction power, it's the same thing as taking the denominator root of the base to the numerator power.

Basically, this becomes

$\sqrt[4]{x^3}$. (The numerator is what we raise x to the power of, the denominator is the root we take of that).

Hope this helped!