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Simplify. Express your answer using positive exponents.\newline(5u)(2u9)(5u)(2u^9)

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Q. Simplify. Express your answer using positive exponents.\newline(5u)(2u9)(5u)(2u^9)
  1. Identify Components: Identify the components of the expression.\newlineWe have two factors, 5u5u and 2u92u^9, which we need to multiply together. We will group the coefficients (55 and 22) and the powers of uu (uu and u9u^9) separately.
  2. Multiply Coefficients: Multiply the coefficients.\newlineMultiply the numerical coefficients 55 and 22 together.\newline5×2=105 \times 2 = 10
  3. Apply Product Rule: Apply the product rule for exponents.\newlineWhen multiplying powers with the same base, we add the exponents. Since uu has an implied exponent of 11, we have u1×u9u^1 \times u^9.\newlineu1×u9=u(1+9)=u10u^1 \times u^9 = u^{(1+9)} = u^{10}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe found that 5×2=105 \times 2 = 10 and u1×u9=u10u^1 \times u^9 = u^{10}. Now we combine these results to write the expression in its simplest form.\newline(5u)(2u9)=10×u10=10u10(5u)(2u^9) = 10 \times u^{10} = 10u^{10}

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