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Simplify. Express your answer using positive exponents.\newline10c5c4\frac{10c}{5c^4}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline10c5c4\frac{10c}{5c^4}
  1. Write Expression: Write down the expression to be simplified. 10c5c4\frac{10c}{5c^4}
  2. Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression.\newlineDivide 1010 by 55.\newline105=2\frac{10}{5} = 2
  3. Apply Quotient Rule: Apply the quotient rule for exponents to simplify the variable part of the expression.\newlineThe quotient rule states that when dividing like bases, you subtract the exponents.\newlinecc4=c1−4=c−3\frac{c}{c^4} = c^{1-4} = c^{-3}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline2⋅c−32 \cdot c^{-3}\newlineHowever, the question prompt asks for positive exponents, so we need to rewrite c−3c^{-3} as 1c3\frac{1}{c^3}.\newline2⋅1c3=2c32 \cdot \frac{1}{c^3} = \frac{2}{c^3}

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