a) If you're multiplying by two variables by the same coefficient, you will add the exponents.
Explanation: y^3 = y*y*y. y^11 = y*y*y*y*y*y*y*y*y*y*y. So when you're multiplying them, you are essentially adding the exponents-- y*y*y * y*y*y*y*y*y*y*y*y*y*y
Answer: y^14
b) You will multiply the exponents. Think of the explanation I used for the question before, except you are multiplying y^3 eleven times-- thus you will multiply the exponents.
Answer: y^33
c) You will carry down the exponent to the different coefficients.
Explanation: Think of it this way, (3a^4b)(3a^4b) and solve using FOIL and the explanations from the other questions.
Sub-Answer: 9a^8b^2 * (2ba^4)^3
So by doing the same thing to the other half of the equation, the next sub-answer would be:
9a^8b^2 * 8a^12b^3
So now, you would add the exponents with the same coefficients, but multiply the coefficients like you normally would. Your complete answer is: 72a^20b^5.
If you have any more problems, go to Wolframalpha.com
-Anonymous