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      <text>1.2.4.1 Negative indices</text>
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      <text><![CDATA[<h3>Negative indices
</h3>
<p>Sometimes a number is raised to a negative power. This is interpreted as follows:</p>

<div class="HELM_keypoint">
<h4>Key Point <br></h4>
<p><strong>Negative Powers</strong></p>
<p>\(a^{-m} = \dfrac{1}{a^m}, \qquad a^m = \dfrac{1}{a^{-m}}\)</p>
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<p>Thus a negative index can be used to indicate a reciprocal.</p>

<hr>
<h4 class="HELM_example">Example <br></h4>
<p>Write each of the following expressions using a positive index and simplify if possible.</p>
<ol class="HELM_parts_inline">
<li>\(2^{-3}\)</li>
<li>\(\dfrac{1}{4^{-3}}\)</li>
<li>\(x^{-1}\)</li>
 <li>\(x^{-2}\)</li>
<li>\(10^{-1}\)</li>
</ol>


<h4 class="HELM_solution">Solution</h4>
<ol class="HELM_parts">
<li> \(2^{-3} = \dfrac{1}{2^3} = \dfrac{1}{8}\)</li>
 <li> \(\dfrac{1}{4^{-3}} = 4^3 = 64\)</li>
 <li>\(x^{-1}= \dfrac{1}{x^1}=\dfrac{1}{x}\)</li>
 <li>\(x^{-2}= \dfrac{1}{x^2}\)</li>
  <li>\(10^{-1}=\dfrac{1}{10^1}= \dfrac{1}{10} \) or \( 0.1\)</li>
</ol>]]></text>
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