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Simplify. Express your answer using positive exponents.\newline2d2d7\frac{2d^2}{d^7}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline2d2d7\frac{2d^2}{d^7}
  1. Write Expression: Write down the expression.\newlineThe expression given is 2d2d7\frac{2d^2}{d^7}. We need to simplify this expression.
  2. Apply Quotient Rule: Apply the quotient rule for exponents. The quotient rule states that when dividing powers with the same base, we subtract the exponents. 2d2d7=2×d(2−7)\frac{2d^2}{d^7} = 2 \times d^{(2-7)}
  3. Subtract Exponents: Perform the subtraction of the exponents.\newlineSubtract the exponents 22 and 77.\newlined(2−7)=d−5d^{(2-7)} = d^{-5}
  4. Simplify Expression: Simplify the expression.\newlineNow we have 2⋅d−52 \cdot d^{-5}. Since we want to express the answer using positive exponents, we can write d−5d^{-5} as 1/d51/d^5.\newline2⋅d−5=2d52 \cdot d^{-5} = \frac{2}{d^5}
  5. Final Answer: Write the final simplified expression.\newlineThe final simplified expression is 2d5.\frac{2}{d^5}.

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