Answer:
[tex]\sqrt[4]{x^3}[/tex]
Step-by-step explanation:
First, let's examine our original statement.
[tex]x^{\frac{1}{2} }\cdot x^{\frac{1}{4}}[/tex]
Using exponent rules, we know that if we have [tex]x^a \cdot x^b[/tex], then simplified, the answer will be equivalent to [tex]x^{a+b}[/tex].
So we can simplify this by adding the exponents [tex]\frac{1}{2}[/tex] and [tex]\frac{1}{4}[/tex].
Converting [tex]\frac{1}{2}[/tex] into fourths gets us [tex]\frac{2}{4}[/tex].
[tex]\frac{2}{4} + \frac{1}{4} = \frac{3}{4}[/tex].
So we now have [tex]x^{\frac{3}{4}}[/tex].
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
[tex]\sqrt[4]{x^3}[/tex]. (The numerator is what we raise x to the power of, the denominator is the root we take of that).
Hope this helped!
