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Simplify. Express your answer using positive exponents.\newline5c65c\frac{5c^6}{5c}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline5c65c\frac{5c^6}{5c}
  1. Write Problem: Write down the problem.\newlineWe have the expression 5c65c\frac{5c^6}{5c}.
  2. Simplify Coefficients: Simplify the coefficients.\newlineBoth the numerator and the denominator have a coefficient of 55, so they cancel each other out.\newline55=1\frac{5}{5} = 1
  3. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineWhen dividing powers with the same base, we subtract the exponents.\newlinec6/c1=c(6−1)=c5c^6/c^1 = c^{(6-1)} = c^5
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineSince the coefficients cancel out to 11, we are left with c5c^5.\newlineSo, 5c65c\frac{5c^6}{5c} simplifies to c5c^5.

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