Here's the question you clicked on:
JetWave600
How do I express 1/5x^3 using inverse notation?
|dw:1342726354928:dw|
You mean like how \(\large \frac{1}{x}\) = x\(^{-1}\) ???
I guess so, the answer is (1/5)x^-3, but I want to know why that is the answer.
|dw:1342727173036:dw|
If you want to know why you should graph both 1/x and x^-1 :-) \(y_1 = \frac{1}{x}\) \(y_2 = x^{-1}\) Input a few values and you will see they are identical. when x=1, the output for each is? when x=2? when x=3? A negative on the exponent is the same as a fraction. If you want to get even more technical than that it's going to pull on some very difficult for me to explain higher-math proofs. \(\large x^{\text{- anything}} = \frac{1}{\text{anything}}\) The constant is just one fifth. \[\frac{1}{5x^3} = \frac{1}{5} * \frac{1}{x^3}=\frac{1}{5}*x^{-3}\]
Welcome to OpenStudy btw :-D Here's our community's rules if you were curious: http://openstudy.com/code-of-conduct Does this make a bit more sense now? If not, then start graphing the first few point from 1 to 5 for these two. (put in 1 for x, get something out for 5, then plot the coordinate)
I'm understanding a bit more, but what if the denominator is like x+5?
\[\frac{1}{x+5} = (x+5)^{-1}\]
FYI: As you can see the parenthesis become very important to ensure you're adding THEN using the exponent. Otherwise it's just x+\(\frac{1}{5}\) which is wrong lol. We should always be able to go forwards or reverse in mathematics. That's very common mistake for many people, forgetting "( )", so get into the practice of using parenthesis around polynomials when you can to help you out :-)
A lot more sense then the rest of the internet.
Well if that made sense to you then you should also learn this, it's extremely helpful from Algebra onward & upward! \(\large \sqrt{x} = x^{\frac{1}{2}}\) \(\large \sqrt[3]{x} = x^{\frac{1}{3}}\) \(\large \sqrt[4]{x} = x^{\frac{1}{4}}\) etc... \(\large \frac{1}{\sqrt{x}} = x^{-\frac{1}{2}}\) \(\large \frac{1}{\sqrt[3]{x}} = x^{-\frac{1}{3}}\) \(\large \frac{1}{\sqrt[4]{x}} = x^{-\frac{1}{4}}\) etc... Roots are just fractional powers! Negative powers are just inverses (fractions with 1 divided by something) Learn this well and you'll find things to be much easier :-)
Four possible situations: positive, normal exponent (i.e.: x^2) negative, normal exponent (your question here) positive, fractional exponent (same thing as a root) negative, fractional exponent (1 divided by said root, an inverse root) That's everything for how exponents work :-)
Thanks for everything!
Good luck out there! And I hope you can really get this property down :-D It helps, don't skip it