On this page you will find videos on rational exponents and roots that are not square roots.

1. $\rhd$ Simplifying rational exponents (number) (3:49)  Simplify $\frac{256^{\frac{4}{7}}}{2^{\frac{4}{7}}}$.
2. $\rhd$ Simplifying rational exponent expressions (one variable) (2:31)  Simplify $m^{\frac{7}{9}}m^{\frac{1}{3}}$
3. $\rhd$ Simplifying rational exponent expressions: mixed exponent and radicals (2:38)  (Notice the constraint on the value of $v$!)  Leveraging laws of exponents to re-write $v^{(\frac{-6}{5})} \cdot \sqrt{v} = v^k$ for $k$ an integer and $v \geq 0$
4. $\star$ Simplifying rational exponent expressions
5. $\rhd$ Simplifying radical terms (two variables) (2:15) Simplify $\sqrt{125x^6y^3}$
6. $\rhd$ Simplifying radical expressions with multiplication (4:24) $5\sqrt{2x^2} \cdot 3 \sqrt{4x^4}$
7. $\rhd$ Simplifying a radical expression with two variables (division) (3:06) $\frac{\sqrt{60x^2y}}{\sqrt{48x}}$
8. $\star$ Simplifying radical expressions such as $\frac{\sqrt{2}}{\sqrt{-128}}$
9. $\rhd$ Simplifying mixed radical and exponential expressions (7:31) $(r^{\frac{2}{3}}s^3)^2 \sqrt{20r^4s^5}$
10. $\rhd$ Simplifying rational exponent expressions (advanced) (6:06) $\frac{125^{\frac{-1}{8}}125^{\frac{5}{8}}}{5^{\frac{1}{2}}}$
11. $\star$ Simplifying rational exponent expressions (advanced) For $x>0$ and $y>0$, find $u$ such that $\frac{(65x^5y^6)^{\frac{5}{7}}}{\sqrt{(5x^3y^4)^3}\sqrt{(13x^2y^2)^3}} = \sqrt[u]{65x^5y^6)^2}$

And if you feel you would like to see more examples, here are some optional videos.

1. $\rhd$ Simplifying radical terms (4:15) Sal simplifies $3\sqrt{500x^3}$.
2. $\rhd$ Simplifying mixed radicals and exponents (2:50) $6^{\frac{1}{2}} \cdot (\sqrt{6})^3$
3. $\rhd$ Simplifying radical expressions (three variables) (5:25) $\sqrt{27a^2b^5c^3} = 3bc\sqrt{a^2b^2}$