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      <text>1.2.2.3 Laws of indices cont</text>
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      <text><![CDATA[<p>Two important results which can be derived from the laws of indices state:</p>
<div class="HELM_keypoint">
<h4>Key Point <br></h4>

<ul>
<li>Any non-zero number raised to the power \(0\) has the value \(1\) , that is \(a^0=1\).</li>
<li>Any number raised to power \(1\) is itself, that is \(a^1=a\).</li>
</ul>
</div>
<p>A generalisation of the third law of indices states:</p>
<div class="HELM_keypoint">
<h4>Key Point <br></h4>
<p>\((a^mb^n)^k = a^{mk}b^{nk}\) .</p>
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<hr>
<h4 class="HELM_example">Example <br></h4>
<p>Remove the brackets from</p>
<ol class="HELM_parts_inline">
<li>\((3x)^2\)</li>
<li>\((x^3y^7)^4\)</li>
</ol>
<h4 class="HELM_solution">Solution</h4>
<ol class="HELM_parts">
  <li>Noting that \(3=3^1\) and \(x=x^1\) then \((3x)^2= (3^1x^1)^2 = 3^2x^2=9x^2\). <br> Alternatively \((3x)^2=(3x)\times (3x) = 9x^2\).</li>
  <li>\((x^3y^7)^4 = x^{3\times 4}y^{7\times 4} = x^{12}y^{28}\).</li>
  </ol><p>&nbsp;</p>
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