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Simplify. Express your answer using positive exponents.\newline6qq5\frac{6q}{q^5}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline6qq5\frac{6q}{q^5}
  1. Write Given Expression: Write down the given expression.\newlineThe given expression is 6qq5\frac{6q}{q^5}. We need to simplify this expression by dividing the terms.
  2. Apply Quotient Rule: Apply the quotient rule for exponents. The quotient rule states that when dividing powers with the same base, you subtract the exponents. In this case, we have q1q^1 in the numerator and q5q^5 in the denominator, so we subtract the exponents. 6qq5=6×q1−5\frac{6q}{q^5} = 6 \times q^{1-5}
  3. Perform Exponent Subtraction: Perform the subtraction of the exponents.\newlineSubtract the exponents 11 and 55.\newlineq(1−5)=q−4q^{(1-5)} = q^{-4}
  4. Simplify Expression: Simplify the expression.\newlineNow we have 6×q−46 \times q^{-4}. Since we want to express the answer using positive exponents, we can write q−4q^{-4} as 1q4\frac{1}{q^4}.\newline6×q−4=6×1q4=6q46 \times q^{-4} = 6 \times \frac{1}{q^4} = \frac{6}{q^4}
  5. Write Final Expression: Write the final simplified expression.\newlineThe final simplified expression is 6/q46/q^4.

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