One way to start is to flip the entire "schmegegy" (4x^2 y) to the denominator whilst changing the exponent of -2 to a +2.
Another is to use "power of a power" to impact the same schmegegy, updating it to (4^-2 x^-4 y^-2) and then flip the relevant factors to the denominator.
If you think this is a doozie, I guess you haven't peeked ahead to #27-28!!
Jesus - the only factors that "flip" are the ones with the negative exponents. The xy^2 stays where it is, since it is in the denominator with a positive exponent.
Our "target" when we simplify algebraic fractions is to rid ourselves of the negative exponents and then reduce to lowest form where possible. Negative exponents in the numerator "flip" to the denominator and become positive exponents. Negative exponents in the denominator "flip" to the numerator and become positive. Factors with positive exponents stay where they are.
From the standpoint of the numerical coefficients, the 6 stays "up top" and the 4^-2 "goes down" and becomes 4^2 or 16. Therefore the 6/16 ultimately reduces to the 3/8 that you see in the answer above.
Tough to see where you're going wrong. My suspicion is that you are flipping more than what is being called for. For example, for the xy^-3 in the first fraction's denominator, only the y factor will flip... the x factor has an exponent of 1, so it stays put. Do you understand that (in this case) the -3 applies only to the 'y' and not the 'x'?
6 comments:
#26 is a doozy. Pg. 416 #26.
6x^-2 y^2 X (4x^2 y)^-2
----------- ------------
xy^-3 xy^2
I got the beginning of it, but, I would appreciate any other people's way of starting it. Any thoughts helpful!!!
╟ §o §olicits §ovalius╢
One way to start is to flip the entire "schmegegy" (4x^2 y) to the denominator whilst changing the exponent of -2 to a +2.
Another is to use "power of a power" to impact the same schmegegy, updating it to (4^-2 x^-4 y^-2) and then flip the relevant factors to the denominator.
If you think this is a doozie, I guess you haven't peeked ahead to #27-28!!
wait so for #26, if u flip the (4x^2y)^-2
-----------
xy^2
you get: xy^2
------
(4x^2y)^2
right or did I do something wrong and do I flip
6x^-2y^2
---------
xy^-3 ??????
Jesus - the only factors that "flip" are the ones with the negative exponents. The xy^2 stays where it is, since it is in the denominator with a positive exponent.
Our "target" when we simplify algebraic fractions is to rid ourselves of the negative exponents and then reduce to lowest form where possible. Negative exponents in the numerator "flip" to the denominator and become positive exponents. Negative exponents in the denominator "flip" to the numerator and become positive. Factors with positive exponents stay where they are.
Hope this helps.
-Mr. C
I did #26 slowly and step by step and i got
20 x^2 y^4 is that right?
'fraid not.
The answer is 3y/8x^8.
From the standpoint of the numerical coefficients, the 6 stays "up top" and the 4^-2 "goes down" and becomes 4^2 or 16. Therefore the 6/16 ultimately reduces to the 3/8 that you see in the answer above.
Tough to see where you're going wrong. My suspicion is that you are flipping more than what is being called for. For example, for the xy^-3 in the first fraction's denominator, only the y factor will flip... the x factor has an exponent of 1, so it stays put. Do you understand that (in this case) the -3 applies only to the 'y' and not the 'x'?
Not sure if that helps you.
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