Question

\frac{\sqrt4{b}}{\sqrt{b}}

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Convert radicals to rational exponents

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

$$ \sqrt{b} = b^{\frac{1}{2}} $$

The expression becomes:

$$ \frac{b^{\frac{1}{4}}}{b^{\frac{1}{2}}} $$

Step 2: Apply the quotient rule of exponents

Subtract the exponent in the denominator from the exponent in the numerator:

$$ b^{\frac{1}{4} - \frac{1}{2}} = b^{\frac{1}{4} - \frac{2}{4}} = b^{-\frac{1}{4}} $$

Step 3: Write with positive exponents or in radical form

Using positive exponents:

$$ \frac{1}{b^{\frac{1}{4}}} $$

Using radical notation:

$$ \frac{1}{\sqrt[4]{b}} $$

Answer:

$$ b^{-\frac{1}{4}} \text{ or } \frac{1}{b^{\frac{1}{4}}} \text{ or } \frac{1}{\sqrt[4]{b}} $$