Solution 1.3:4a

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Because the base is the same in both factors, the exponents can be combined according to the power rules
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<center> [[Image:1_3_4a.gif]] </center>
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<math>2^{9}\centerdot 2^{-7}=2^{9-7}=2^{2}=4</math>
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Alternatively, the expressions for the powers can be expanded completely and then cancelled out,
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<math>\begin{align}
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& 2^{9-7}=2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot \frac{1}{2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2} \\
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& \\
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& =2\centerdot 2=4 \\
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\end{align}</math>

Revision as of 11:45, 15 September 2008

Because the base is the same in both factors, the exponents can be combined according to the power rules


\displaystyle 2^{9}\centerdot 2^{-7}=2^{9-7}=2^{2}=4


Alternatively, the expressions for the powers can be expanded completely and then cancelled out,


\displaystyle \begin{align} & 2^{9-7}=2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot \frac{1}{2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2} \\ & \\ & =2\centerdot 2=4 \\ \end{align}

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