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Simplify. Express your answer using positive exponents. \newline9u4(u)(3u)\frac{9u^4}{(u)(3u)}

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Simplify exponential expressions using the multiplication and division rulesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline9u4(u)(3u)\frac{9u^4}{(u)(3u)}
  1. Write Expression and Group: Write down the expression and group the coefficients and variables. 9u4u(3u)=(9u)⋅(u43u)\frac{9u^4}{u(3u)} = \left(\frac{9}{u}\right) \cdot \left(\frac{u^4}{3u}\right)
  2. Simplify Coefficients: Simplify the coefficients.\newline9u\frac{9}{u} can be simplified to 99, since dividing by uu and then multiplying by uu cancels out.\newline\left(\frac{\(9\)}{u}\right) \times \left(\frac{u^\(4\)}{\(3\)u}\right) = \(9 \times \left(\frac{u^44}{33u}\right)
  3. Simplify Variables: Simplify the variables.\newlineWhen dividing powers with the same base, we subtract the exponents.\newlineu43u=u4−1=u3\frac{u^4}{3u} = u^{4-1} = u^3
  4. Combine Coefficients and Variables: Combine the simplified coefficients and variables. 9×(u43u)=9×u39 \times \left(\frac{u^4}{3u}\right) = 9 \times u^3
  5. Write Final Expression: Write the final simplified expression.\newline9×u3=9u39 \times u^3 = 9u^3

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