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Example 1
For all real numbers x, y and z where y and z are not equal to zero,
$\dfrac{ \sqrt[3]{64 x^6 y^3 z^9 } } {\sqrt[3]{8 y^6 z^6}}=$
- $2\dfrac{x^2 z}{y}$
- $=2 x^2 z y$
- $\dfrac{8}{3}\dfrac{x^2 z}{y}$
- $2\dfrac{x^3 z^2}{y}$
- $2\dfrac{x^3 y}{z^2}$
Solution
This example is about simplifying expressions including powers and radicals.
- We first rewrite the given expression using one radical only as follows
$\dfrac{ \sqrt[3]{64 x^6 y^3 z^9 } } {\sqrt[3]{8 y^6 z^6}}=\sqrt[3] {\dfrac {64 x^6 y^3 z^9}{8 y^6 z^6}}$
- We now simplify the expression, with exponents, under the radical
$=\sqrt[3] {\dfrac {8 x^6 z^3}{y^3}}$
- Take the cube root of the expression under the radical
$=2\dfrac{x^2 z}{y}$
Answer A
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