I'm supposed 2 simplify this, and according to my Barron's Precalc The EZ way, the answer is B^n.
So far, I've not gotten there, but hopefully I will soon. So far, I've not had issues with this problem set, but for some reason, this one and the next one (same type of problem) are stumping me.
I will continue working with this and hopefully will get it, soon. I suspect that I need to start with the paranthetical cube in the numerator, but I feel like I'm 15 yrs old again (I'm in my 40s ☺) staring at my text book. Good grief, and this was my idea to try this book on for size.
Plato, thank you: among my multi-solutions that I've come up with, your is the most logical, but not anything like the 2 or 3 that I came up with, and certainly not the "B^n" the Barron's EZ precalc gives as the answer. I'm going to study how to deal with exponents, and then come back to this section of questions in the book.
Please note: a^(b^c) is NOT the same as (a^b)^c. Exponentiation is NOT associative.
Are you sure that the initial equation isn't supposed to mean instead? If it does, then the answer would indeed be b^n.
Note that (a^b)^c = a^(b*c)
The fundamental property of exponents, valid everywhere, is that . So when b is negative, this leads to . Make use of this property
I'll double-check the book tonite, and make sure I've entered and am showing it correctly, as in the opening thread. I'm pretty sure I copied it and got it right, and i used MathOMir to turn it into an image: but just in case, I want to be sure. I understand both examples you two have given, and will look for more samples online to play with. My Barrons book only has two in this format (at least in this section of the book.)
SworD, you are correct: I mis-keyed the equation. I see on my paper-work where I was first attempting it, I copied it correctly, but still worked it incorreclty. A few days later, on paper, I had copied it again, thinking I'd start over on it and do better, but I miswrote it down. From that, I used mathomir, and that is why the problem appears as such at the start of the thread.
► So, you are correct, the numerator is (b^2n+1)^3 All in parantheses, cubed. ◄
Armed with the above comments, I will try this problme again, on my own. Thanks for the help, folks.