Question

If x≠0, which expression is equivalent to this expression?



x3√4x112

Answer 1

Answer:

$x^{\frac{2}{3}}$

Step-by-step explanation:

Given:

$\frac{\sqrt[4]{x^3}}{x^{\frac{1}{12}}}$

Required:

Equivalent expression of the above expression if x ≠ 0

Solution:

$\frac{\sqrt[4]{x^3}}{x^{\frac{1}{12}}}$

Applying lower rule of exponents, rewrite the numerator

$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{12}}}$

Next, apply the Quotient rule of exponents

$x^{\frac{3}{4} - \frac{1}{12}}$

$x^{\frac{9 - 1}{12}}$

$x^{\frac{8}{12}}$

$x^{\frac{2}{3}}$

Answer 2

We want to find an expression that is equivalent to the given one, we will see that the equivalent expression is:

$x^{2/3}$

Two properties will be used here, these are:

$\sqrt[n]{a} ^m = a^{m/n}$

and

$\frac{a^n}{a^m} = a^{n - m}$

Now, we start with the expression:

$\frac{\sqrt[4]{x^3} }{x^{1/12}}$

With the first property, we can rewrite the numerator as:

$\frac{\sqrt[4]{x^3} }{x^{1/12}} = \frac{x^{3/4} }{x^{1/12}}$

Now we use the second property to get:

$\frac{x^{3/4} }{x^{1/12}} = x^{3/4 - 1/12} = x^{2/3}$

Then the correct option is the third one, counting from the top.

If you want to learn more, you can read:

https://brainly.com/question/24443453