Solution 1.3:1d

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Current revision (12:50, 22 September 2008) (edit) (undo)
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By using the power rules, we can rewrite the expression,
By using the power rules, we can rewrite the expression,
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{{Displayed math||<math>\left( \frac{2}{3} \right)^{-3} = \frac{2^{-3}}{3^{-3}} = \frac{\,\dfrac{1}{2^{3}}\,}{\,\dfrac{1}{3^{3}}\,} = \frac{\,\dfrac{1}{2^{3}}\cdot 3^{3}\,}{\,\dfrac{1}{\rlap{\,/}3^{3}}\cdot {}\rlap{\,/}3^{3}\,} = \frac{\,\dfrac{3^{3}}{2^{3}}\,}{1} = \frac{3^{3}}{2^{3}}\,,</math>}}
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<math>\left( \frac{2}{3} \right)^{-3}=\frac{2^{-3}}{3^{-3}}=\frac{\frac{1}{2^{3}}}{\frac{1}{3^{3}}}=\frac{\frac{1}{2^{3}}\centerdot 3^{3}}{\frac{1}{3^{3}}\centerdot 3^{3}}=\frac{\frac{3^{3}}{2^{3}}}{1}=\frac{3^{3}}{2^{3}}</math>
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and then carry out the calculation
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and then carry out the calculation:
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{{Displayed math||<math>\frac{3^{3}}{2^{3}} = \frac{3\cdot 3\cdot 3}{2\cdot 2\cdot 2} = \frac{27}{8}\,</math>.}}
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<math>\frac{3^{3}}{2^{3}}=\frac{3\centerdot 3\centerdot 3}{2\centerdot 2\centerdot 2}=\frac{27}{8}</math>
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Current revision

By using the power rules, we can rewrite the expression,

\displaystyle \left( \frac{2}{3} \right)^{-3} = \frac{2^{-3}}{3^{-3}} = \frac{\,\dfrac{1}{2^{3}}\,}{\,\dfrac{1}{3^{3}}\,} = \frac{\,\dfrac{1}{2^{3}}\cdot 3^{3}\,}{\,\dfrac{1}{\rlap{\,/}3^{3}}\cdot {}\rlap{\,/}3^{3}\,} = \frac{\,\dfrac{3^{3}}{2^{3}}\,}{1} = \frac{3^{3}}{2^{3}}\,,

and then carry out the calculation

\displaystyle \frac{3^{3}}{2^{3}} = \frac{3\cdot 3\cdot 3}{2\cdot 2\cdot 2} = \frac{27}{8}\,.
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