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Simplify the expression: (5^(-2) * 10^(-4)) / (2^(-5) * 5^(-6))
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Solution: Step 1: Apply exponent rules for division and multiplication Step 2: (5^(-2) * 10^(-4)) / (2^(-5) * 5^(-6)) = (5^(-2) * (2*5)^(-4)) / (2^(-5) * 5^(-6)) Step 3: Simplify using exponent properties: (5^(-2) * 2^(-4) * 5^(-4)) / (2^(-5) * 5^(-6)) Step 4: Combine like terms: (5^(-6) * 2^(-4)) / (2^(-5) * 5^(-6)) Step 5: Cancel out common factors: 2^(-4 + 5) = 2^1 = 2 Step 6: Therefore, the value of the expression is 2.
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