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5 votes
What is the product?

(3a^2b^7)(5a^3b^8)

User Ente
by
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1 Answer

3 votes

Answer: 15a^5b^15

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Step-by-step explanation:

The coefficients of each term are 3 and 5. They are the first things mentioned in each parenthesis grouping. The coefficients multiply to 3*5 = 15. This is the coefficient of the final answer.

The 'a' terms are a^2 and a^3. They multiply to a^2*a^3 = a^(2+3) = a^5. Add the exponents because we're using the rule a^b*a^c = a^(b+c). The base must be the same for this rule to apply.

The b terms are b^7 and b^8. They multiply to b^7*b^8 = b^(7+8) = b^15

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To summarize

  • The coefficients multiply to 15.
  • The 'a' terms multiply to a^5
  • The b terms multiply to b^15

This is how we end up with 15a^5b^15 as the final answer

User John Kramlich
by
4.1k points