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Chapter 6: Chapter 6

Problem 67

Next question

Simplify (a) \(3^{-2}\) (b) \(1 / 5^{-2}\)

Short Answer

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The simplified expressions are: (a) \(3^{-2} = \frac{1}{9}\) (b) \(\frac{1}{5^{-2}} = 25\)
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Simplify expression (a) \(3^{-2}\)

First, we can rewrite the expression using the property of negative exponents: \[3^{-2} = \frac{1}{3^2}\] Now, simply calculate the exponent: \[\frac{1}{3^2} = \frac{1}{9}\] So, \(3^{-2} = \frac{1}{9}\).

Step 2: Simplify expression (b) \(\frac{1}{5^{-2}}\)

First, we can rewrite the expression using the property of negative exponents: \[\frac{1}{5^{-2}} = \frac{1}{\frac{1}{5^2}}\] Now, we can simplify the expression further by multiplying the numerator and the denominator of the inner fraction by \(5^2\): \[\frac{1}{\frac{1}{5^2}} = \frac{1 \times 5^2}{1}\] Lastly, calculate the exponent: \[\frac{1 \times 5^2}{1} = \frac{25}{1} = 25\] So, \(\frac{1}{5^{-2}} = 25\).

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