Chapter 1: Q. 202 (page 53)

Simplify $\frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}}$

Short Answer

Expert verified

On simplifying the given expression, we get

$\frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = 32$

Step by step solution

Step 1. Given information

$\begin{array}{l} Theexpressiongivenis \\ \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} \\ Wehavetosimplifythegivenexpression. \end{array}$

Step 2. Simplify the numerator and denominator

$\begin{array}{l} \Rightarrow \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = \frac{(3 \times 3 \times 3) - (3 \times 3)}{(\frac{3^{2}}{4^{2}})} \\ \Rightarrow \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = \frac{27 - 9}{(\frac{9}{16})} \\ \Rightarrow \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = \frac{18}{(\frac{9}{16})} \end{array}$

Step 3. Simplify the fraction

$\begin{array}{l} \Rightarrow \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = \frac{18}{(\frac{9}{16})} \\ \Rightarrow \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = \frac{18 \times 16}{9} \\ \Rightarrow \frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}} = \frac{9 \times 2 \times 16}{9} \\ = 32 \end{array}$

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Simplify $\frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the numerator and denominator

Step 3. Simplify the fraction

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Simplify33-32342

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the numerator and denominator

Step 3. Simplify the fraction

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Simplify $\frac{3^{3} - 3^{2}}{{(\frac{3}{4})}^{2}}$