Simplify Exponents and Radicals

Example on how to simplify expressions with exponents and radicals. .

Example 1


For all real numbers x, y and z where y and z are not equal to zero,

$\dfrac{ \sqrt[3]{64 x^6 y^3 z^9 } } {\sqrt[3]{8 y^6 z^6}}=$



  1. $2\dfrac{x^2 z}{y}$
  2. $=2 x^2 z y$
  3. $\dfrac{8}{3}\dfrac{x^2 z}{y}$
  4. $2\dfrac{x^3 z^2}{y}$
  5. $2\dfrac{x^3 y}{z^2}$

Solution

This example is about simplifying expressions including powers and radicals.

  1. We first rewrite the given expression using one radical only as follows

    $\dfrac{ \sqrt[3]{64 x^6 y^3 z^9 } } {\sqrt[3]{8 y^6 z^6}}=\sqrt[3] {\dfrac {64 x^6 y^3 z^9}{8 y^6 z^6}}$


  2. We now simplify the expression, with exponents, under the radical

    $=\sqrt[3] {\dfrac {8 x^6 z^3}{y^3}}$

  3. Take the cube root of the expression under the radical

    $=2\dfrac{x^2 z}{y}$

    Answer A