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Simplify. Express your answer using positive exponents.\newline5w95w\frac{5w^9}{5w}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline5w95w\frac{5w^9}{5w}
  1. Write and Group: Write down the expression and group the coefficients and powers that have the same base.\newline5w95w=(55)⋅(w9w1)\frac{5w^9}{5w} = \left(\frac{5}{5}\right) \cdot \left(\frac{w^9}{w^1}\right)
  2. Simplify Coefficients: Simplify the coefficients. 55=1\frac{5}{5} = 1
  3. Simplify Powers: Simplify the powers of ww using the quotient rule for exponents (subtract the exponents).w9w1=w(9−1)=w8\frac{w^9}{w^1} = w^{(9-1)} = w^8
  4. Combine Coefficients and Powers: Combine the simplified coefficients and powers of ww.55×w9w1=1×w8=w8\frac{5}{5} \times \frac{w^9}{w^1} = 1 \times w^8 = w^8

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