Answer:
First problem: [tex]x^{1/2}[/tex]
Second problem: no
Step-by-step explanation:
For the first problem, [tex]\sqrt[3]{x}\cdot \sqrt[6]{x}[/tex] can be rewritten into [tex]x^\frac{1}{3}\cdot x^\frac{1}{6}[/tex].
Recall that when you multiply numbers that have the same base, you just add up the exponents. Therefore:
[tex]x^\frac{1}{3}\cdot x^\frac{1}{6}=x^{\frac{1}{6}+\frac{1}{3}} = x^\frac{1}{2}[/tex]
For the second problem, the answer is no. The reason for that is because when you multiply numbers that have the same base, you don't multiply the exponents. Instead, you add the exponents.
