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Simplify. Express your answer using positive exponents.\newline(2m4)(8m9)(2m^4)(8m^9)

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline(2m4)(8m9)(2m^4)(8m^9)
  1. Group coefficients and powers: Group the coefficients and the powers with the same base.\newline(2m4)(8m9)(2m^4)(8m^9) can be written as (2×8)×(m4×m9)(2 \times 8) \times (m^4 \times m^9).
  2. Multiply coefficients: Multiply the coefficients.\newline2×8=162 \times 8 = 16.
  3. Apply product rule for exponents: Apply the product rule for exponents, which states that when multiplying powers with the same base, you add the exponents.\newlinem4×m9=m(4+9)=m13m^4 \times m^9 = m^{(4+9)} = m^{13}.
  4. Combine results: Combine the results from Step 22 and Step 33 to write the expression in its simplest form.\newline(2m4)(8m9)=(2×8)×(m4×m9)=16×m13=16m13(2m^4)(8m^9) = (2 \times 8) \times (m^4 \times m^9) = 16 \times m^{13} = 16m^{13}.

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