Answer:
Step-by-step explanation:
Before we do anything, we need to write this question from written form into expression form.
"The product of the cube root of x squared times the 4th root of x cubed" is:
[tex](\sqrt[3]{x^{2}})(\sqrt[4]{x^{3} } )[/tex]
The best way to solve this is if you know the properties of exponents. The first thing to do is to convert these square roots and squares into exponents using the fractional exponent rule:
[tex]a^{\frac{m}{n} } =\sqrt[n]{a^{m} }[/tex]
[tex]= (x^{\frac{2}{3} } )(x^{\frac{3}{4} } )[/tex]
Now, we can combine these two using the product rule:
[tex](a^{m} )(a^{n} )=(a^{m+n} )[/tex]
[tex]= x^{\frac{2}{3} } + x^{\frac{3}{4} } = x^{\frac{17}{12} } or \sqrt[12]{x^{17} }[/tex]
