Multiplication of Radicals

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[5]{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[3]{125x^6y^3}
  6.  \rhd Simplifying radical expressions with multiplication (4:24) 5\sqrt[3]{2x^2} \cdot 3 \sqrt[3]{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[3]{2}}{\sqrt[3]{-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[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.

  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[5]{6})^3
  3. \rhd Simplifying radical expressions (three variables) (5:25) \sqrt[3]{27a^2b^5c^3} = 3bc\sqrt[3]{a^2b^2}