Simplifying 7^-2(-3)^2
This problem involves simplifying an expression with negative exponents and squares. Here's a step-by-step breakdown:
Understanding the Rules
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Negative exponents: A number raised to a negative exponent is equivalent to its reciprocal raised to the positive version of that exponent.
- Example: 7^-2 = 1/7^2
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Squares: Squaring a number means multiplying it by itself.
- Example: (-3)^2 = (-3) * (-3) = 9
Applying the Rules
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Simplify (-3)^2: (-3)^2 = 9
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Simplify 7^-2: 7^-2 = 1/7^2 = 1/49
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Combine the results: 7^-2(-3)^2 = (1/49) * 9 = 9/49
Final Answer
Therefore, the simplified form of 7^-2(-3)^2 is 9/49.
