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Simplify. Express your answer using positive exponents.\newline8m2m3\frac{8m}{2m^3}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline8m2m3\frac{8m}{2m^3}
  1. Write Expression: Write down the given expression.\newlineWe have the expression 8m2m3\frac{8m}{2m^3}.
  2. Simplify Coefficients: Simplify the coefficients.\newlineDivide the coefficients 88 by 22.\newline82=4\frac{8}{2} = 4
  3. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineWhen dividing powers with the same base, subtract the exponents.\newlinem1/m3=m(1−3)=m−2m^{1} / m^{3} = m^{(1-3)} = m^{-2}
  4. Express with Positive Exponents: Express the answer with positive exponents.\newlineSince we need to express the answer with positive exponents, we rewrite m−2m^{-2} as 1m2\frac{1}{m^2}.
  5. Combine Results: Combine the results from Step 22 and Step 44.\newlineThe simplified expression is 4×1m24 \times \frac{1}{m^2}, which can be written as 4m2\frac{4}{m^2}.

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