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<h4>Evaluating Exponential Expressions</h4>
<p>A power is repeated multiplication of the same factor. The factor is the base, and the number of times the base is used as a factor is the exponent. The expression is called a power. </p>
<p> \(Base\rightarrow\underbrace{5^3}^{\leftarrow Exponent}\) </p>
<p>The expression \(5^3\) is read:</p>
<ul>
<li> five to the power of three </li>
<li> five to the third power </li>
<li> five cubed </li>
</ul>
<p>\(5^3\) means 5 is used as a factor 3 times: \(5^3 =5 \cdot 5 \cdot 5=125\).</p>
<p>Evaluate each expression.</p>
<ol class="os-raise-noindent">
<li> \((\frac{1}{2})^5\) <br>
<br>
Use \(\frac12\) as a factor 5 times.<br>
<br>
\((\frac{1}{2})^5 =\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}=\frac{1}{32}\)<br>
<br>
\((\frac{1}{2})^5 =\frac{1}{32}\)<br>
<br>
</li>
<li> \(7(3)^4\) <br>
<br>
Use order of operations. Evaluate the exponent first. <br>
<br>
\(7(3)^4 =7(3 \cdot 3 \cdot 3 \cdot 3)=7(81)\)<br>
<br>
Then multiply.<br>
<br>
\(7(81)=567\)<br>
<br>
\(7(3)^4 =567\)
</li>
</ol>
<ol class="os-raise-noindent" start="3">
<li> \(20(0.8)^2\) <br>
<br>
Use order of operations. Evaluate the exponent first. <br>
<br>
\(20(0.8)^2 =20(0.8 \cdot 0.8)=20(0.64)\)<br>
<br>
Then multiply.<br>
<br>
\( 20(0.64)=12.8\)<br>
<br>
\( 20(0.8)^2 =12.8\)
</li>
</ol>
<h4> Try It: Evaluating Exponential Expressions</h4>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<p>Evaluate \(50(0.2)^2\).</p>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer. Then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answer:</p>
<p>Here is how to evaluate this exponential expression.</p>
<p><strong>Step 1</strong> - Use order of operations and evaluate the power first. <br>
\(50(0.2)^2 =50(0.2 \cdot 0.2)=50(0.04)\)</p>
<p><strong>Step 2</strong> - Next, multiply.<br>
\(50(0.04)=2\)<br>
\(50(0.2)^2 =2\)</p>
</div>
<br>
<h4>Check Your Understanding</h4>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="5a651857-1ba7-45dc-bfcf-a246bb8c0447" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
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<div class="os-raise-ib-pset-problem" data-content-id="a282e7d5-8ff3-48ff-bde9-7d135038dcfe" data-problem-type="multiplechoice" data-solution="54" data-solution-options='["27", "216", "18", "54"]'>
<div class="os-raise-ib-pset-problem-content">
<p>Evaluate \(2(3)^3\).</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Check yourself: Use order of operations and evaluate the power first. Then multiply the result by 2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Try again. Let’s try again in a different way: Use order of operations and evaluate the power first. Then multiply the result by \(2\).</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 54.</p>
</div>
</div>
<!--END QUESTION.-->
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<div class="os-raise-ib-pset-correct-response">
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</div>
<div class="os-raise-ib-pset-encourage-response">
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