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Simplify. Express your answer using positive exponents.\newline(7t)(3t5)(7t)(3t^5)

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Q. Simplify. Express your answer using positive exponents.\newline(7t)(3t5)(7t)(3t^5)
  1. Identify Components: Identify the components of the expression.\newlineWe have two factors, 7t7t and 3t53t^5, which need to be multiplied together. Both factors contain the variable tt, so we can use the property of exponents that states when multiplying like bases, we add the exponents.
  2. Multiply Coefficients: Multiply the coefficients (numbers in front of the variables).\newlineMultiply 77 by 33 to get the coefficient for the final expression.\newline7×3=217 \times 3 = 21
  3. Apply Exponent Rule: Apply the exponent rule for multiplying like bases.\newlineSince tt has an implied exponent of 11 in the first term (7t7t), we add the exponents of tt from both terms.\newlinet1×t5=t(1+5)=t6t^1 \times t^5 = t^{(1+5)} = t^6
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have the coefficient 2121 from Step 22 and the variable with its exponent t6t^6 from Step 33. Combine these to get the final simplified expression.\newline21×t6=21t621 \times t^6 = 21t^6

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