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Problem 67

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

Expert verified
The simplified expressions are: (a) $$3^{-2} = \frac{1}{9}$$ (b) $$\frac{1}{5^{-2}} = 25$$
See the step by step solution

## 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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