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Simplify. Express your answer using positive exponents.\newline(2s4)(5s9)(2s^4)(5s^9)

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline(2s4)(5s9)(2s^4)(5s^9)
  1. Group coefficients and powers: Group the coefficients and powers that have the same base.\newline(2s4)(5s9)(2s^4)(5s^9) can be written as (2×5)×(s4×s9)(2 \times 5) \times (s^4 \times s^9).
  2. Multiply coefficients: Multiply the coefficients.\newline2×5=102 \times 5 = 10.
  3. Apply product rule for exponents: Apply the product rule for exponents to combine s4s^4 and s9s^9. According to the product rule, when multiplying powers with the same base, you add the exponents. s4×s9=s4+9=s13s^4 \times s^9 = s^{4+9} = s^{13}.
  4. Combine results for simplest form: Combine the results from Step 22 and Step 33 to write the expression in its simplest form.\newline(2s4)(5s9)=10×s13=10s13(2s^4)(5s^9) = 10 \times s^{13} = 10s^{13}.

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