## anonymous one year ago MEDAL = FAN What value of c solves the equation?

1. anonymous

2. Nnesha

remember this exponent rule $\huge\rm x^{-m}=\frac{ 1 }{ x^{-m} }$ if there is negative exponent then you should flip the fraction.

3. anonymous

what do you men by flip the fraction?

4. anonymous

mean**

5. freckles

I know it was just a type-o :p $x^{-m}=\frac{1}{x^{\color{red}m}}$

6. Nnesha

like in this example x^{-m} is same as x^{-m} over one $\huge\rm \frac{ x^{-m }}{ 1 }= \frac{ 1 }{ x^m }$ in other words reciprocal of x^{-m}/1 is 1/x^m

7. Nnesha

2/3 when you flip it you will get 3/2 right ?

8. anonymous

Yes.

9. anonymous

So if I flip, I will get $\frac{ 16 }{ 1 }$

10. anonymous

If that's what you mean

11. Nnesha

that's exactly how u should flip the fraction but i meant to say that c should be negative so that's 4^c is equal to 1 over 16

12. Nnesha

$\huge\rm \frac{ 4^{-c} }{ 1 }= \frac{ 1 }{ 16 }$ $\frac{ 4^{-c} }{ 1 } = ?$

13. anonymous

And how do i figure out 4-^c?

14. Nnesha

let's do the other way $\huge\rm 4^c =16$ reciprocal of 1/6 is 16 now 4 to the what power = 16?

15. Nnesha

1/16**

16. anonymous

the 3rd?

17. Nnesha

4^3 is same 4 times 4 times 4 which is not equalto 16

18. anonymous

my mistake, 4^2.

19. anonymous

does c = 2?

20. Nnesha

actually my bad first we write it in exponent form and then we should flip it i'm sorry $\huge\rm 4^c=\frac{ 1 }{ 4^2 }$ now flip the fraction when you do that sign would change

21. Nnesha

$\huge\rm 4^c= 4^{-2}$ now cancel out 4

22. anonymous

C=-2?

23. Nnesha

yes right

24. Nnesha

now just to check ur answer substitute c for -2 $\frac{ 4^{-2} }{ 1 }=\frac{ 1 }{ 16 }$both sides re equal good to go! remember there is negative exponent so don't forget to flip the fraction :P