<h3>Laws of indices</h3><p>An <strong>index</strong> (plural indices) is a power. The key laws are:</p><ul><li><code>a^m x a^n = a^(m+n)</code> (multiply: add the indices)</li><li><code>a^m ÷ a^n = a^(m-n)</code> (divide: subtract the indices)</li><li><code>(a^m)^n = a^(mn)</code> and <code>a^0 = 1</code></li></ul><h3>Standard form</h3><p><strong>Standard form</strong> (scientific notation) writes a number as <code>A x 10^n</code> where A is at least 1 but less than 10. For example <code>45000 = 4.5 x 10^4</code> and <code>0.0072 = 7.2 x 10^-3</code>.</p><h3>Logarithms</h3><p>A <strong>logarithm</strong> to base ten answers: <em>10 to what power gives this number?</em> Since <code>10^2 = 100</code>, we say <code>log 100 = 2</code>. A log has a whole-number part called the <strong>characteristic</strong> and a decimal part called the <strong>mantissa</strong>. Logs let us multiply by adding logs and divide by subtracting them.</p><div class="callout"><strong>Kenyan context:</strong> Kenya's population is about 53 million people. In standard form that is <code>5.3 x 10^7</code>. A single grain of maize might weigh about <code>0.0003</code> kg, which is <code>3 x 10^-4</code> kg. Writing both in standard form makes them easy to compare and compute with.</div>