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Simplify. Express your answer using positive exponents. \newline4u6u⋅4u\frac{4u^6}{u \cdot 4u}

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Q. Simplify. Express your answer using positive exponents. \newline4u6u⋅4u\frac{4u^6}{u \cdot 4u}
  1. Write & Simplify Expression: Write down the expression and simplify the coefficients and variables separately. \newline4u6u×4u\frac{4u^6}{u \times 4u} can be rewritten as 4u64u2\frac{4u^6}{4u^2} since u×4uu \times 4u is the same as 4u24u^2.
  2. Simplify Coefficients: Simplify the coefficients.\newlineThe coefficient 44 in the numerator and denominator cancels out because 44\frac{4}{4} equals 11.\newlineSo, 4u64u2\frac{4u^6}{4u^2} becomes u6u2\frac{u^6}{u^2}.
  3. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineWhen dividing powers with the same base, subtract the exponents: u6/u2=u(6−2)=u4u^6/u^2 = u^{(6-2)} = u^4.
  4. Write Final Expression: Write the final simplified expression.\newlineThe expression 4u6u⋅4u\frac{4u^6}{u \cdot 4u} simplifies to u4u^4.

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