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Simplify. Express your answer using positive exponents.\newline2d2d3\frac{2d}{2d^3}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline2d2d3\frac{2d}{2d^3}
  1. Simplify expression by dividing: Simplify the expression 2d2d3\frac{2d}{2d^3} by dividing the coefficients and subtracting the exponents of like bases.\newlineWhen dividing powers with the same base, we subtract the exponents.\newline2d2d3=22×d1d3\frac{2d}{2d^3} = \frac{2}{2} \times \frac{d^1}{d^3}
  2. Divide the coefficients: Divide the coefficients. 22=1\frac{2}{2} = 1
  3. Subtract exponents of dd: Subtract the exponents of dd.d1d3=d(1−3)=d−2\frac{d^1}{d^3} = d^{(1-3)} = d^{-2}Since we want to express the answer using positive exponents, we take the reciprocal of d−2d^{-2} to make the exponent positive.d−2=1d2d^{-2} = \frac{1}{d^2}
  4. Combine the results: Combine the results from Step 22 and Step 33.\newline1×1d2=1d21 \times \frac{1}{d^2} = \frac{1}{d^2}

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