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Simplify. Express your answer using positive exponents.\newline4d4d7\frac{4d}{4d^7}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline4d4d7\frac{4d}{4d^7}
  1. Divide and Subtract Exponents: Simplify the expression by dividing the coefficients and subtracting the exponents.\newlineGiven the expression 4d4d7\frac{4d}{4d^7}, we can divide the coefficients (4/4)(4/4) and use the quotient rule for exponents, which states that when you divide like bases, you subtract the exponents (d1−d7)(d^1 - d^7).\newline4d4d7=(44)⋅(d1−7)\frac{4d}{4d^7} = (\frac{4}{4}) \cdot (d^{1-7})
  2. Perform Division and Subtraction: Perform the division of the coefficients and the subtraction of the exponents.\newlineThe division of the coefficients 44\frac{4}{4} equals 11, and subtracting the exponents (1−7)(1-7) gives us −6-6.\newlineSo, 4d4d7=1×d(−6)\frac{4d}{4d^7} = 1 \times d^{(-6)}
  3. Express Answer with Positive Exponents: Express the answer using positive exponents.\newlineSince we want the answer with positive exponents, we can rewrite d−6d^{-6} as 1/d61/d^6.\newlineTherefore, the simplified expression is 1/d61/d^6.

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