Simplifying Rational Exponents and Radicals II (Multiplication and Division)

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

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

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

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

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The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.

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The OpenLab at City Tech:A place to learn, work, and share

The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.