## JetWave600 3 years ago How do I express 1/5x^3 using inverse notation?

1. JetWave600

|dw:1342726354928:dw|

2. agentx5

You mean like how $$\large \frac{1}{x}$$ = x$$^{-1}$$ ???

3. JetWave600

I guess so, the answer is (1/5)x^-3, but I want to know why that is the answer.

4. JetWave600

|dw:1342727173036:dw|

5. agentx5

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. $\frac{1}{5x^3} = \frac{1}{5} * \frac{1}{x^3}=\frac{1}{5}*x^{-3}$

6. agentx5

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)

7. JetWave600

I'm understanding a bit more, but what if the denominator is like x+5?

8. agentx5

$\frac{1}{x+5} = (x+5)^{-1}$

9. agentx5

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 :-)

10. agentx5

Make sense?

11. JetWave600

A lot more sense then the rest of the internet.

12. agentx5

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 :-)

13. agentx5

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 :-)

14. JetWave600

Thanks for everything!

15. agentx5

Good luck out there! And I hope you can really get this property down :-D It helps, don't skip it