Help with expressions!
- Thread starter alocke06
- Start date
mmm4444bot
Super Moderator
- Joined
- Oct 6, 2005
- Messages
- 10,962
Hello A Locke:
Since you made no statements about what you already know, or why you're stuck, or what you're thinking, or what you've tried, or what you don't understand about these exercises, your lessons, or your textbook, I have no way of knowing where you're at.
So, I'm guessing that the following is good enough, for you.
If you want specific help from volunteers at this web site, then you'll need to ask specific questions.
Let's start with a basic property of exponents that all algebra students should memorize.
(a*b)^n = a^n * b^n
In other words, this property tells us that each factor in the product xy gets raised to the fourth power.
\(\displaystyle (xy)^4 = x^4 y^4\)
The form x^P y^Q - x^R y^S requires us to eventually rewrite the given (single) ratio as a difference of two (separate) ratios. I'll do that right now.
\(\displaystyle \frac{x^3 y^7 - x^5}{x^4 y^4} = \frac{x^3 y^7}{x^4 y^4} - \frac{x^5}{x^4 y^4}\)
We can next factor each of these two terms to get fractional factors involving powers of the same base (i.e., x over x, and y over y).
\(\displaystyle \frac{x^3}{x^4} \cdot \frac{y^7}{y^4} - \frac{x^5}{x^4} \cdot \frac{y^0}{y^4}\)
(Hopefully, you understand why I put y^0 in the rightmost numerator above.)
To finish, it's simply a matter of using another property of exponents that all algebra students should memorize.
a^n/a^m = a^(n - m)
In other words, if powers' bases are the same in a ratio, then we simplify by subtracting the lower exponent from the upper exponent.
For example, here's how to determine P.
\(\displaystyle \frac{x^3}{x^4} = x^{3 - 4} = x^{-1}\)
P = -1
For the second exercise, you need to use another property of exponents.
x^n * x^m = x^(n + m)
For example, we have x^2 * x^P = x^6, so x^(2 + P) must equal x^6.
Show some work or ask some questions on your own, if you would like more help.
Cheers ~ Mark
