it was quite confusing at first but i later understood it.

<h2>Simplifying Expressions with Exponents</h2>
<p>Remember that an exponent indicates repeated multiplication of the same quantity. For example, \({2}^{4}\) means to multiply four factors of \(2,\) so \({2}^{4}\) means \(2·2·2·2.\) This format is known as <strong>exponential notation</strong>.</p>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Definition: Exponential Notation</h3>
<img alt="On the left side, a raised to the m is shown. The m is labeled in blue as an exponent. The a is labeled in red as the base. On the right, it says a to the m means multiply m factors of a. Below this, it says a to the m equals a times a times a times a, with m factors written below in blue." src="https://data.ulearngo.com/assets/f20e0944-8545-46a1-934a-1d741924388e"/>
<p>This is read \(a\) to the \({m}^{\mathrm{th}}\) power.</p>
</div>
</div>
<p>In the expression \({a}^{m},\) the <strong>exponent</strong> tells us how many times we use the <strong>base</strong> \(a\) as a factor.</p>
<p><img alt="On the left side, 7 to the 3rd power is shown. Below is 7 times 7 times 7, with 3 factors written below. On the right side, parentheses negative 8 to the 5th power is shown. Below is negative 8 times negative 8 times negative 8 times negative 8 times negative 8, with 5 factors written below." src="https://data.ulearngo.com/assets/b0641549-4c69-4f20-af16-618d43da0002"/></p>
<p>Before we begin working with variable expressions containing exponents, let’s simplify a few expressions involving only numbers.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Simplify:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}{5}^{3}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}{9}^{1}\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\({5}^{3}\)</td>
</tr>
<tr>
<td>Multiply 3 factors of 5.</td>
<td>\(5·5·5\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(125\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\({9}^{1}\)</td>
</tr>
<tr>
<td>Multiply 1 factor of 9.</td>
<td>\(9\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Simplify:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}{\left(\frac{7}{8}\right)}^{2}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}{\left(0.74\right)}^{2}\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\({\left(\frac{7}{8}\right)}^{2}\)</td>
</tr>
<tr>
<td>Multiply two factors.</td>
<td>\(\left(\frac{7}{8}\right)\left(\frac{7}{8}\right)\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(\frac{49}{64}\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\({\left(0.74\right)}^{2}\)</td>
</tr>
<tr>
<td>Multiply two factors.</td>
<td>\(\left(0.74\right)\left(0.74\right)\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(0.5476\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Simplify:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}{\left(-3\right)}^{4}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}{-3}^{4}\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\({\left(-3\right)}^{4}\)</td>
</tr>
<tr>
<td>Multiply four factors of −3.</td>
<td>\(\left(-3\right)\left(-3\right)\left(-3\right)\left(-3\right)\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(81\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\({-3}^{4}\)</td>
</tr>
<tr>
<td>Multiply two factors.</td>
<td>\(-\left(3·3·3·3\right)\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(-81\)</td>
</tr>
</tbody>
</table>
<p>Notice the similarities and differences in parts and . Why are the answers different? In part the parentheses tell us to raise the (−3) to the 4<sup>th</sup> power. In part we raise only the 3 to the 4<sup>th</sup> power and then find the opposite.</p>
</div>
</div>
</div>
</div>
</div>

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Simplifying Expressions with Exponents

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

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Discover how to identify, determine the degree of, add, subtract, multiply, divide, and factor polynomials while also simplifying expressions with exponents in this tutorial.


Simplifying Expressions with Exponents

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