Radicals and Fractional Exponents
Name: _________________________
Date: __________________________
Worked-Out Examples
Example 1: Evaluate
\( 27^{\frac{2}{3}} \)
\(\rightarrow (\sqrt[3]{27})^2\)
\(\rightarrow (3)^2\)
\(\rightarrow 9\)
Example 2: Rewrite
\( (\sqrt[5]{x})^3 \)
\(\rightarrow \text{Root is 5, Power is 3}\)
\(\rightarrow x^{\frac{3}{5}}\)
Practice Problems
Rewrite each expression in the requested form, or evaluate it completely.
1. Rewrite \( y^{\frac{1}{5}} \) in radical form.
2. Rewrite \( \sqrt[3]{a} \) in exponent form.
3. Evaluate \( 100^{\frac{1}{2}} \)
4. Rewrite \( b^{\frac{2}{5}} \) in radical form.
5. Rewrite \( (\sqrt{k})^3 \) in exponent form.
6. Evaluate \( 16^{\frac{3}{4}} \)
7. Rewrite \( (2x)^{\frac{1}{2}} \) in radical form.
8. Rewrite \( (\sqrt[6]{m})^5 \) in exponent form.
9. Evaluate \( 4^{\frac{5}{2}} \)
10. Rewrite \( c^{\frac{7}{4}} \) in radical form.
11. Rewrite \( \sqrt[3]{x^2} \) in exponent form.
12. Evaluate \( 125^{\frac{2}{3}} \)