## anonymous one year ago can someone help me find the power form of the reciprocal radical form 1/(3 sqrt.three(x^2))

1. anonymous

$\frac{ 1 }{ 3\sqrt[3]{x ^{2}}}$

2. anonymous

you have a simple formula for radicals $\sqrt[a]{x^b}=x^\frac{b}{a}$|dw:1444074783490:dw|

3. anonymous

Also $x^n=\frac{1}{x^{-n}} \space \space \space ; \space \space \space \frac{1}{x^n}=x^{-n}$ Just add a minus sign to the exponent when u move the number from numerator to denominator or vice versa

4. anonymous

|dw:1444075056599:dw|

5. anonymous

@Johan14th r u there?

6. anonymous

yes so then it would be x^ 2/3

7. anonymous

$3x^{\frac{ 2 }{ 3 }}$

8. anonymous

no! you're not done yet!!

9. anonymous

$\frac{1}{3x^{\frac{2}{3}}}$

10. anonymous

We need to bring the number to the top now!! |dw:1444075590776:dw|

11. anonymous

oh okay so then it is $3x^{\frac{- 3 }{ 2 }}$

12. anonymous

and then i could apply the power rule right?

13. anonymous

Hmm, you only change the sign, you leave the fraction unchanged, also the number 3 will stay in the bottom, if you want to bring the 3 to the top, you must write -1 to it's power $\frac{1}{3x^{\frac{2}{3}}}=\frac{x^{-\frac{2}{3}}}{3}=3^{-1}x^{-\frac{2}{3}}$

14. anonymous

okay so basically adding the (-) to the power makes it go on to the top of the fraction, numerator. if i want to do the same to the 3 (too get rid of the fraction) i add the (-) to the power

15. anonymous

Yes, anytime you bring a number or letter from top to bottom, or from bottom to top, you change the sign of it's power, very important, remember this rule

16. anonymous

for example if we had $\frac{1}{3^{-1}}$ If we bring it to the top it becomes $\frac{1}{3^{-1}}=3^{1}=3$

17. anonymous

okay that just cleared everything out. thank you. i was trying too do some weird multiplication. you saved me!

18. anonymous

you're absolutely welcome