Fractional Exponents and Radicals

Definition of Square Root

Which of the following statements about $\sqrt{4}$ is correct?

Nth Roots and Cube Roots

Evaluate $\sqrt[3]{27}$.

Connecting Fractional Exponents and Radicals

Evaluate $8^{\frac{2}{3}}$.

Handling Negative Fractional Exponents

Evaluate $16^{-\frac{3}{4}}$.

Laws of Fractional Exponents

Simplify $a^{\frac{1}{2}}\cdot a^{\frac{1}{3}}$ (for $a>0$), writing the result in the form $a^{p/q}$.

Power of a Power with Fractional Exponents

Evaluate $(27^{\frac{2}{3}})^{\frac{1}{2}}$.

Disentangling Common Look-Alikes

Simplify $\sqrt{a^{2}}$ for any real number $a$.

Which of the following identities is true?

Simplify $\sqrt{8}$, writing the result in the form $a\sqrt{b}$.

Write $\sqrt[3]{a^{2}}$ in fractional exponent form, and write $a^{-\frac{1}{2}}$ in radical form.

Why do the five exponent laws continue to hold for rational exponents?

Fractional Exponents and Radicals: Key Takeaways