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Chapter 6: Chapter 6

Problem 68

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Simplify the following expressions: (a) \(-3^{-2}\) (b) \((-3)^{-2}\) (c) \(-3 / 4^{-1}\)

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\( -3^{-2} = \frac{1}{9} \) \( (-3)^{-2} = \frac{1}{9} \) \( -3 / 4^{-1} = -\frac{3}{4} \)
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Understand negative exponents

For any nonzero number a, a^{-n} is equal to 1 divided by a^n. This means -3^{-2} = 1/(-3^2).

Step 2: Apply exponent rules

Now we need to calculate the square of -3: (-3)^2 = (-3) * (-3) = 9. So, -3^{-2} = 1/9. #a) Answer:# \( -3^{-2} = \frac{1}{9} \) #b) Simplify (-3)^{-2}#

Step 1: Understand negative exponents

As before, we have a{-n} equal to 1 divided by a^n, which means that (-3)^{-2} = 1/((-3)^2).

Step 2: Apply exponent rules

Now we need to calculate the square of -3: (-3)^2 = (-3) * (-3) = 9. So, (-3)^{-2} = 1/9. #b) Answer:# \( (-3)^{-2} = \frac{1}{9} \) #c) Simplify -3 / 4^{-1}#

Step 1: Understand negative exponents

Again, for any nonzero number a, a^{-n} is equal to 1 divided by a^n. So, 4^{-1} = 1/4.

Step 2: Simplify expression

Now we have -3 divided by 4^{-1}, which is equal to -3 * (1/4), since dividing by a fraction is the same as multiplying by its reciprocal.

Step 3: Compute the product

Finally, we can compute the product: -3 * (1/4) = -3/4. #c) Answer:# \( -3 / 4^{-1} = -\frac{3}{4} \)

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