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Simplify. Express your answer using positive exponents.\newline(6w)(2w)(8w4)(6w)(2w)(8w^4)

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Q. Simplify. Express your answer using positive exponents.\newline(6w)(2w)(8w4)(6w)(2w)(8w^4)
  1. Identify Components: Identify the components of the expression (6w)(2w)(8w4)(6w)(2w)(8w^4). We have 33 terms that are being multiplied together. Each term consists of a coefficient and a power of ww.
  2. Group Coefficients and Powers: Group the coefficients and the powers of ww.(6w)(2w)(8w4)(6w)(2w)(8w^4) can be rewritten as (6×2×8)×(w×w×w4)(6 \times 2 \times 8) \times (w \times w \times w^4).
  3. Multiply Coefficients: Multiply the coefficients.\newline6×2×86 \times 2 \times 8 equals 9696.
  4. Apply Product Rule: Apply the product rule for exponents to the powers of ww. The product rule states that when multiplying powers with the same base, you add the exponents. So w×w×w4w \times w \times w^4 becomes w(1+1+4)w^{(1+1+4)}.
  5. Simplify Exponent: Simplify the exponent for ww.w(1+1+4)w^{(1+1+4)} simplifies to w6w^6.
  6. Combine Coefficient and Power: Combine the simplified coefficient and power of ww. The expression (6w)(2w)(8w4)(6w)(2w)(8w^4) simplifies to 96×w696 \times w^6, which can be written as 96w696w^6.

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