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Simplify. Express your answer using positive exponents. \newline8d22d⋅d2\frac{8d^2}{2d \cdot d^2}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline8d22d⋅d2\frac{8d^2}{2d \cdot d^2}
  1. Divide and Apply Quotient Rule: Simplify the expression by dividing the coefficients and applying the quotient rule for exponents.\newlineThe quotient rule for exponents states that when you divide like bases, you subtract the exponents. In this case, we have d2d^2 in the numerator and d1⋅d2d^1 \cdot d^2 in the denominator. First, we divide the coefficients 88 by 22, which gives us 44. Then we apply the quotient rule to the exponents of dd.\newline8d22d⋅d2=4d2−1−2\frac{8d^2}{2d \cdot d^2} = 4d^{2-1-2}
  2. Perform Exponent Subtraction: Continue simplifying the expression by performing the subtraction of the exponents. \newline4d(2−1−2)=4d(2−3)4d^{(2-1-2)} = 4d^{(2-3)}
  3. Simplify Exponent: Simplify the exponent by performing the subtraction. 4d2−3=4d−14d^{2-3} = 4d^{-1}
  4. Convert Negative Exponent: Express the negative exponent as a positive exponent by writing it as a reciprocal.\newlineA negative exponent means that the base is on the wrong side of the fraction line, so we flip it to make the exponent positive.\newline4d−1=4d4d^{-1} = \frac{4}{d}

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