Chapter 4 - Polynomials - 4.1 Exponents and Their Properties - 4.1 Exercise Set - Page 237: 108

$\dfrac{16}{375}$

Work Step by Step

Using the laws of exponents, the given expression $\dfrac{\left( \dfrac{1}{2} \right)^3\left( \dfrac{2}{3} \right)^4}{\left( \dfrac{5}{6} \right)^3}$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{8}\cdot\dfrac{16}{81}\div\dfrac{125}{216} \\\\= \dfrac{1}{8}\cdot\dfrac{16}{81}\cdot\dfrac{216}{125} \\\\= \dfrac{1}{\cancel{8}}\cdot\dfrac{\cancel{8}\cdot2}{\cancel{27}\cdot3}\cdot\dfrac{\cancel{27}\cdot8}{125} \\\\= \dfrac{16}{375} .\end{array}

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