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Which is equal to 568256^{-82}?\newlineChoices:\newline(A) (56)82(-56)^{82}\newline(B) 15682\frac{1}{56^{82}}\newline(C) 568256^{82}\newline(D) 15682\frac{1}{56^{-82}}

Full solution

Q. Which is equal to 568256^{-82}?\newlineChoices:\newline(A) (56)82(-56)^{82}\newline(B) 15682\frac{1}{56^{82}}\newline(C) 568256^{82}\newline(D) 15682\frac{1}{56^{-82}}
  1. Understand expression: Understand the expression 568256^{-82}. Identify the base and the exponent. In 568256^{-82}, 5656 is the base raised to the exponent 82-82. Base: 5656 Exponent: 82-82
  2. Identify base and exponent: Apply the negative exponent rule.\newlineThe negative exponent rule states that am=1ama^{-m} = \frac{1}{a^m}.\newlineTherefore, 568256^{-82} can be rewritten as 15682\frac{1}{56^{82}}.
  3. Apply negative exponent rule: Match the rewritten expression with the given choices.\newlineThe expression 1/56821 / 56^{82} matches choice (B) 1/56821/56^{82}.