## anonymous 5 years ago ok, i need to simplyfy this and show all working: 3^3 / sqrt3^5

1. anonymous

$3^{3}\div \sqrt{3^{5}}$

2. nowhereman

You should use $\sqrt{x} = x^{\frac{1}{2}}$

3. anonymous

how

4. nowhereman

use power rules, and $\frac{x}{y} = x\cdot y^{-1}$

5. nowhereman

You do have the same bases there, so all you need no know then is what $x^a \cdot x^b$ is

6. anonymous

oh, so it will be like $3^{3-(1/5)}$ right?

7. nowhereman

nearly, but: $\left( x^a \right) ^b = x^{a\cdot b}$

8. anonymous

$\sqrt{3^{5}} = 3^{1/5} . so you get 3^{3}/$

9. anonymous

you get 3^3 / 3^1/5

10. anonymous

sqrt3

11. anonymous

hence that will be $3^{3-1/5}$

12. nowhereman

that is exactly the mistake! $\sqrt{3^5} = \left( 3^5 \right)^{\frac{1}{2}}$

13. anonymous

oh no i think i get it wrong. that should be 3^5/2

14. anonymous

hence, its $3^{3-}$

15. anonymous

16. anonymous

its 3^3-5/2 = 3^1/2

17. nowhereman

And just for completeness, $x^{\frac{1}{5}} = \sqrt[5]{x}$

18. anonymous

the answer is $\sqrt{3}$ right?

19. anonymous

duc, how do you get sqrt3?

20. anonymous

I know the answere, but I dont know how to get to the answer

21. anonymous

$3^{3-5/2}$

22. anonymous

ok, guys, i appreciate you helping me, i just became your fan

23. anonymous

First , You 3^5=3*3^4, so SQRT(3^5)=SQRT(3)*3^2,===>(3^3)/(SQRT(3)*3^2)=3/SQRT(3)=SQRT(3) It may be TRUE

24. anonymous

ok, thankyou

25. anonymous

No problem() good luck