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Simplify. Express your answer using positive exponents. \newline(4u6)(5u7)(8u)(4u^6)(5u^7)(8u)

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Q. Simplify. Express your answer using positive exponents. \newline(4u6)(5u7)(8u)(4u^6)(5u^7)(8u)
  1. Multiply Coefficients: Multiply the coefficients (numerical parts) of the terms.\newlineWe have 44, 55, and 88 as coefficients. Multiplying these gives us:\newline4×5×8=20×8=1604 \times 5 \times 8 = 20 \times 8 = 160
  2. Apply Product Rule: Apply the product rule for exponents to the variables.\newlineThe product rule states that when multiplying like bases, you add the exponents. We have u6u^6, u7u^7, and u1u^1 (since uu is the same as u1u^1). Adding these exponents gives us:\newline6+7+1=146 + 7 + 1 = 14\newlineSo, u6×u7×u=u6+7+1=u14u^6 \times u^7 \times u = u^{6+7+1} = u^{14}
  3. Combine Results: Combine the results from Step 11 and Step 22 to get the final simplified expression.\newlineWe have the coefficient 160160 from Step 11 and the variable part u14u^{14} from Step 22. Combining these gives us:\newline160u14160u^{14}