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Simplify. Express your answer using positive exponents.\newline9n93n\frac{9n^9}{3n}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline9n93n\frac{9n^9}{3n}
  1. Divide and Subtract Exponents: Divide the coefficients and subtract the exponents.\newlineDivide 99 by 33 and subtract the exponent of nn in the denominator from the exponent of nn in the numerator.\newline9n93n=(93)⋅(n9n1)\frac{9n^9}{3n} = (\frac{9}{3}) \cdot (\frac{n^9}{n^1})
  2. Simplify Coefficients: Simplify the coefficients.\newline93=3\frac{9}{3} = 3.\newline(93)⋅(n9n1)=3⋅(n9n1)\left(\frac{9}{3}\right) \cdot \left(\frac{n^9}{n^1}\right) = 3 \cdot \left(\frac{n^9}{n^1}\right)
  3. Subtract Exponents: Subtract the exponents of nn. When dividing powers with the same base, subtract the exponents. n9/n1=n(9−1)=n8n^9 / n^1 = n^{(9-1)} = n^8
  4. Combine Coefficients and Powers: Combine the simplified coefficients and powers of nn.3×n8=3n83 \times n^8 = 3n^8

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