Answer preview
Actually, 10^27 IS the same as 1/10^-27! This is a common misconception about negative exponents and reciprocals. The key lies in understanding how the negative exponent rule works when you have a fraction with a negative exponent in the denominator.
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How to approach this question
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Step 1: Apply the negative exponent rule to rewrite 1/10^-27
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Step 2: Use the property that 1/a^-n = a^n to simplify the expression
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Step 3: Verify the equality by comparing both expressions in their simplified forms