## anonymous one year ago What is the missing value? https://static.k12.com/bank_packages/files/media/mathml_6a898366c833b4d7194aa8d29fc91e60db252b97_1.gif A. −10 B. −2 C. 2 D. 10

1. anonymous

@jim_thompson5910

2. jim_thompson5910

hint: $\LARGE \frac{x^a}{x^b} = x^{a-b}$

3. anonymous

D 10?

4. jim_thompson5910

$\LARGE \frac{x^a}{x^b} = x^{a-b}$ $\LARGE \frac{3^{-6}}{3^{{}^\boxed{}}} = 3^{4}$ $\LARGE \frac{3^{-6}}{3^{x}} = 3^{4}$ $\LARGE 3^{-6-x} = 3^{4}$ set the exponents equal to one another and solve for x

5. anonymous

You lost me.

6. jim_thompson5910

where at?

7. anonymous

The last part

8. jim_thompson5910

when I went from $\LARGE \frac{3^{-6}}{3^{x}} = 3^{4}$ to $\LARGE 3^{-6-x} = 3^{4}$ ???

9. anonymous

Yes

10. jim_thompson5910

I used that rule I wrote in the hint. When you divide expressions like x^3 over x^2, you subtract the exponents

11. anonymous

Is it a? -10

12. jim_thompson5910

solve -6 - x = 10 for x

13. jim_thompson5910

sorry I meant -6 - x = 4

14. anonymous

negative - a negative = a positive = -6 - (-2) = 4 Right?

15. jim_thompson5910

-6 - (-2) = 4 is false

16. jim_thompson5910

-6 - (-2) = -4 is true so try again

17. anonymous

@jim_thompson5910

18. jim_thompson5910

yes -6 - (-10) = -6 + 10 = 4

19. anonymous

OKAY THANKS

20. jim_thompson5910

no problem