## anonymous one year ago Which of the following expressions are equivalent? Justify your reasoning. Please help Thank you!! A. $^{4\sqrt{x ^{3}}}$ B. $\frac{ 1 }{ x ^{-1} }$ C.$^{10}\sqrt{x ^{5}}\times x ^{4}\times x ^{2}$ D. $x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}$

1. anonymous

@Nnesha hey you think you can help me real quick please?

2. Nnesha

first one is $\huge\rm \sqrt[4]{x^3}$ ?

3. anonymous

Yeah

4. Nnesha

alright you should know some exponent rules for that question when we multiply same bases we should add exponents $\huge\rm x^m \times x^n=x^{m+n}$ $\huge\rm \sqrt[n]{x^m}=x^\frac{ m }{ n }$ you can convert root to an exponent form

5. Nnesha

exponent if there is a negative exponent flip the fraction $\huge\rm x^{-m}=\frac{ 1 }{ x^m }$when you flip the fraction sign of the exponent would change

6. Nnesha

so let's do D first $\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }$

7. anonymous

for the first one it would be changed to |dw:1442352168592:dw|

8. Nnesha

yes right!

9. Nnesha

10. anonymous

would it be |dw:1442352301079:dw|

11. Nnesha

perfecT!

12. Nnesha

can you try c ?

13. Nnesha

first rewrite sqrt{x^5} in exponent form

14. Nnesha

is it $\huge\rm \sqrt[10]{x^5}$ ?

15. anonymous

yeah

16. Nnesha

ok

17. anonymous

would C. be |dw:1442352798917:dw|

18. Nnesha

hmm not write $\huge\rm x^{\frac{ 5 }{ 10 }+4+2}$ when we multiply same bases we should add their exponents so 5/10+4+2 = ?

19. Nnesha

right* not write

20. anonymous

wouldn't it be 11/10

21. Nnesha

hmm no there is denominator so we should find common denomiantor

22. Nnesha

|dw:1442353149290:dw| 4+2 = 6 so 5/10+6/1

23. Nnesha

|dw:1442353207919:dw| it's like cross multiplication but don't forget the positive sign when we find common denominator we should multiply the numerator of 1st fraction by the denominator of 2nd fraction and multiply the numerator of *2nd *fraction by the denominator of first fraction

24. Nnesha

no common denominator is 10 so that would stay the same |dw:1442353470101:dw| like this

25. Nnesha

let me know if you didn't understand that :=)

26. anonymous

would we simplify it or that would be the end

27. Nnesha

simplify that

28. anonymous

65/10

29. Nnesha

reduce the fraction

30. anonymous

13/2

31. anonymous

13/2

32. Nnesha

yes right so x^{13}/2 $\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }$

33. Nnesha

34. anonymous

would it be x^1

35. Nnesha

yes right

36. anonymous

so the two equivalent ones are D. and B.

37. Nnesha

yes right

38. anonymous

thank you again so much

39. Nnesha

yw :=)