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Problem 68

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

Expert verified
$$-3^{-2} = \frac{1}{9}$$ $$(-3)^{-2} = \frac{1}{9}$$ $$-3 / 4^{-1} = -\frac{3}{4}$$
See the step by step solution

## 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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