Question

What is the product of the cube root of x squared times the 4th root of x cubed

Answer 1

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:

`(\sqrt[3]{x^(2)})(\sqrt[4]{x^(3) } )`

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:

`a^{(m)/(n) } =\sqrt[n]{a^(m) }`

`= (x^{(2)/(3) } )(x^{(3)/(4) } )`

Now, we can combine these two using the product rule:

`(a^(m) )(a^(n) )=(a^(m+n) )`

`= x^{(2)/(3) } + x^{(3)/(4) } = x^{(17)/(12) } or \sqrt[12]{x^(17) }`

Answer 2

x^7/12

Explanation:

The question asks what is x^1/3 * x^1/4

x^1/3 * x^1/4

Now with those exponents we can already see that we have the same BASE (x)!! That saves a lot of time.

From there all we do is add the exponents

x ^(1/3 +1/4)

common denominator

x ^(4/12 + 3/12)

x^(7/12)