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Simplify. Express your answer using positive exponents.\newline9q93q\frac{9q^9}{3q}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline9q93q\frac{9q^9}{3q}
  1. Divide and Simplify: Divide the coefficients and simplify the powers with the same base.\newlineDivide the coefficients 99 by 33 and simplify the powers of qq by subtracting the exponents.\newline9q93q=(93)×(q9q1)\frac{9q^9}{3q} = \left(\frac{9}{3}\right) \times \left(\frac{q^9}{q^1}\right)
  2. Calculate Coefficients: Calculate the division of the coefficients.\newline9/3=39 / 3 = 3
  3. Apply Quotient Rule: Apply the quotient rule for exponents which states that when dividing powers with the same base, subtract the exponents. q9/q1=q9−1=q8q^9 / q^1 = q^{9-1} = q^8
  4. Combine Results: Combine the results from Step 22 and Step 33 to write the simplified expression.\newline(9q9/3q)=3×q8=3q8(9q^9 / 3q) = 3 \times q^8 = 3q^8

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