## anonymous 5 years ago How to evaluate -> (5^-4 - 5^-6)/(5^-3 +5^-5)

1. anonymous

bet you got the idea now. write it without the negative exponents. then clear the fractions

2. anonymous

Okay so:

3. anonymous

$\frac{5^{-4} - 5^{-6}}{5^{-3} +5^{-5}}$ muttiply top and bottom by $5^6$

4. anonymous

I got (1/5^4 - 1/5^6)/ (1/5^3 +1/5^5)

5. anonymous

wait. How come I have to multiply top and bottom by 5^6?

6. anonymous

that will clear the fractions. $5^{-4}\times 5^6=5^2$

7. anonymous

if you want you can write this in fraction notation. then you will see that you should multiply top and bottom by $5^6$

8. anonymous

i will write it out if you like

9. anonymous

10. anonymous

$\frac{5^{-4}-5^{-6}}{5^{-3}+5^{-5}}\times \frac{5^6}{5^6}$

11. anonymous

$\frac{5^2-1}{5^3+5}$ is the second line clear?

12. anonymous

pardon?

13. anonymous

i added the exponents, and i chose $5^6$ so that they would all be positive

14. anonymous

okay

15. anonymous

because i want to evaluate the numbers, i need the exponents to be positive

16. anonymous

mmhm

17. anonymous

now i can see what the numbers are. numerator is 25+1=26

18. anonymous

denominator is 125+5=130

19. anonymous

Isn't the numerator 25-1?

20. anonymous

oops yes

21. anonymous

Okay, that's great, thanks :) I was making it way more complicated thn it needed to be

22. anonymous

i would like to say that was a "typo" but i guess it was a mistake. in any case you have the answer, it is $\frac{24}{130}=\frac{12}{65}$

23. anonymous

good! yw

24. anonymous

i like ur pic