SOLUTION: Hi there! I need some help finding out the rule of simplifying the common bases in fractional exponent equations. For example 3 to the 4th power multiplied by 2 to the 3rd power

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Question 605157: Hi there! I need some help finding out the rule of simplifying the common bases in fractional exponent equations. For example 3 to the 4th power multiplied by 2 to the 3rd power over 3 to the 7th power multiplied by 2 to the 2nd power, all raised to the -2 power equals 729/4. I understand how to turn the -2 to a positive 2 exponent by flipping the bottom part of the equation and putting it on top and then moving the top part of the equation to the bottom. What I do not understand is how I find the common bases before raising each factor to the 2nd power. My book shows that 3 to the 7th power becomes 3 to the 3rd power and that the 2 to the 2nd power is completely cancelled out. My book also shows that the 3 to the 4th power is completely cancelled out and that the 2 to the 3rd power becomes 2 to the 1st power. I don't understand how that happened. If they took the 3 to the 7th exponent and the 3 to the 4th exponent and subtracted the exponents (7-4=3), that makes sense. However, what does not make sense to me is that if that is true, then the 2 to the 2nd power and the 2 to the 3rd power should be (2-3= -1); however, the book shows that it is not a -1 exponent, but a positive 1 exponent. What is the rule here? Thank you :)
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!