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Simplify. Express your answer using positive exponents.\newline(4q2)(7q)(4q^2)(7q)

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Q. Simplify. Express your answer using positive exponents.\newline(4q2)(7q)(4q^2)(7q)
  1. Identify Components: Identify the components of the expression that can be combined.\newlineWe have two terms, 4q24q^2 and 7q7q, which can be multiplied together. We will group the coefficients (44 and 77) and the variables with exponents (q2q^2 and qq).
  2. Multiply Coefficients: Multiply the coefficients.\newlineMultiply 44 by 77 to get the coefficient for the final expression.\newline4×7=284 \times 7 = 28
  3. Apply Product Rule: Apply the product rule for exponents.\newlineWhen multiplying powers with the same base, we add the exponents. In this case, we have q2q^2 and qq, which is the same as q1q^1. So we add the exponents 22 and 11.\newlineq2×q1=q(2+1)=q3q^2 \times q^1 = q^{(2+1)} = q^3
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have the coefficient 2828 from Step 22 and the variable with exponent q3q^3 from Step 33. We combine these to get the final simplified expression.\newline28×q3=28q328 \times q^3 = 28q^3

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