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Simplify. Express your answer using positive exponents.\newlined9d9⋅d8\frac{d^9}{d^9 \cdot d^8}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newlined9d9⋅d8\frac{d^9}{d^9 \cdot d^8}
  1. Identify Operation: Identify the operation needed for the exponents.\newlineWhen dividing powers with the same base, we subtract the exponents.
  2. Simplify Expression: Simplify the expression d9/(d9⋅d8)d^9/(d^9 \cdot d^8).\newlineWe can rewrite the denominator as a single power of dd by adding the exponents since they are being multiplied.\newlined9/(d9⋅d8)=d9/d9+8=d9/d17.d^9/(d^9 \cdot d^8) = d^9/d^{9+8} = d^9/d^{17}.
  3. Subtract Exponents: Subtract the exponents.\newlineNow we subtract the exponent in the denominator from the exponent in the numerator.\newlined9/d17=d(9−17)=d−8d^9/d^{17} = d^{(9-17)} = d^{-8}.
  4. Express Answer: Express the answer using positive exponents.\newlineSince the problem asks for positive exponents, we need to rewrite d−8d^{-8} as 1/d81/d^8.\newlineFinal answer: 1/d81/d^8.

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