## MeowLover17 one year ago QUESTION IN COMMENTS

1. MeowLover17
2. MeowLover17

3. MeowLover17

A rectangle has a length of the fifth root of 16 inches and a width of 2 to the 1 over 5 power inches. Find the area of the rectangle.

4. amistre64

5. MeowLover17

Im not sure but i think the answer might be A

6. amistre64

hmm, how are roots and exponents related?

7. MeowLover17

when you transform a root of something to an exponent it will go under 1/?

8. amistre64

yes when an exponent is a fraction, the top is power, the bottom is a root 16^(1/5) * 2^(1/5) is it possible that 16 is a power of 2?

9. MeowLover17

Like $\sqrt{2} =$ 2^1/2

10. MeowLover17

No that is not possible.

11. amistre64

so 2*2*2*2 , cant possible be 16 eh

12. MeowLover17

Or do you mean if i do 2^4

13. MeowLover17

Okay sorry i thought you meant if 16 could go into 2 my bad

14. amistre64

2^4 yes now, lets use this: when an exponent is a fraction the top is a power the bottom is a root 16^(1/5) ... but 16 = 2^4 2^(4/5) now what happens when we multiply like bases?

15. MeowLover17

16. amistre64

ive explained it as basic as i can when an exponent is a fraction ... the TOP is power, the BOTTOM is a root. $\large \sqrt[5]{16}$ $\large \sqrt[5]{2^4}$ $\large {2^{4/5}}$ now all there is to do is multiply to find an area what is: $2^{4/5}~*~2^{1/5}$

17. MeowLover17

2

18. amistre64

right

19. MeowLover17

So my answer would b C

20. amistre64

21. MeowLover17

Thanks for your help i appreciate it :D

22. amistre64

good luck

23. MeowLover17

Would you be able to help me with another one possibly?

24. amistre64

not at the moment

25. MeowLover17

Thanks anyways :D have a great day.