Question

example

\frac{\sqrt4{x}}{\sqrt3{x}}

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Convert radicals to rational exponents

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

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

The expression is:

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

Step 2: Apply the quotient rule of exponents

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

Find a common denominator for the exponents:

$$ \frac{1}{4} - \frac{1}{3} = \frac{3}{12} - \frac{4}{12} = -\frac{1}{12} $$

So, the expression simplifies to:

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

Step 3: Write with a positive exponent or in radical form

Using positive exponents:

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

Using radical notation:

$$ \frac{1}{\sqrt[12]{x}} $$

Answer:

$$ x^{-\frac{1}{12}} \text{ or } \frac{1}{\sqrt[12]{x}} $$