## Amenah8 one year ago Calculus: rewrite 9^2x, base 3

1. phi

can you write 9 as 3 to some power?

2. Amenah8

3^2

3. Amenah8

now what do i do?

4. Amenah8

|dw:1439220479304:dw|

5. anonymous

Replace 9 by 3^2...

6. anonymous

|dw:1439220587021:dw|

7. Amenah8

3^2(2x), base 3?

8. Amenah8

3^4x?

9. phi

did we start with $9^{2x}$ ?

10. anonymous

3^{4x} is good to me..

11. phi

if so then we replace 9 with 3^2 $\left(3^2\right)^{2x}$ and use the rule $\left(a^b\right)^c = a^{b\cdot c}$ to get $3^{2\cdot 2\cdot x} = 3^{4x}$

12. anonymous

$(a^m)^n = (a)^{m \times n}$

13. Amenah8

so sorry something went wrong with my computer. thanks for staying

14. Amenah8

ah! okay i'm back now, sorry

15. Amenah8

so now i have 3^4x, base 3. does the base 3 just mean that, by replacing 9 with 3^2, I got a base of 3? or do i somehow have to apply base 3 to 3^4x?

16. Vocaloid

yeah, you're done. 3^4x is already in base 3, since 3 is being raised to a power

17. Amenah8

thanks so much!! this is just a quick question, but what would i do for a problem like this where i have to make a fraction 1/8 with a base of 2?

18. Vocaloid

similar process, except we're dealing with a negative exponent 1/8 = 1/2^3 = 2^(-3)

19. Amenah8

how did you know it was 1/2^3?

20. Vocaloid

8 = 2^3 therefore 1/8 = 1/2^3

21. Vocaloid

to make a bit more clear 1/8 = 1/(2^3)

22. Amenah8

i get it! thank you os much!!