## anonymous one year ago What value of m solves the equation? 2^m = 1/8

1. anonymous

@ganeshie8

2. anonymous

@pooja195

3. mathstudent55

Have you learned negative exponents?

4. anonymous

doing it now .-. most annoying thing ever.

5. mathstudent55

$$\large a^{-n} = \dfrac{1}{a^n}$$

6. mathstudent55

First, rewrite the fraction 1/8 as 1 over a power of 2. 8 is 2 to what power?

7. mathstudent55

$$\large 2^? = 8$$

8. anonymous

I dont know. ;-;

9. anonymous

10. anonymous

$2 \times 2 = ?$

11. mathstudent55

$$8 = 2 \times 2 \times 2$$ Ok?

12. mathstudent55

How do you write $$2 \times 2 \times 2$$ as 2 raised to an exponent?

13. mathstudent55

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14. mathstudent55

Do you understand now how you write 8 as a power of 2? $$\large 8 = 2 \times 2 \times 2 = 2^3$$

15. anonymous

He's offline.

16. anonymous

im back sorry XD

17. anonymous

18. mathstudent55

Once you know that $$8 = 2^3$$, now you can replace 8 with $$2^3$$ in the fraction. $$\large 2^m = \dfrac{1}{2^3}$$ Ok so far?

19. mathstudent55

Now we look again at the definition of a negative exponent. $$\large a^{-n} = \dfrac{1}{a^n}$$ We have $$\large \dfrac{1}{2^3}$$ Compare the fraction above with the definition of negative exponent.

20. mathstudent55

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21. mathstudent55

The base of the power in the denominator becomes the base. Then the exponent of the denominator becomes the negative of the exponent.

22. mathstudent55

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23. anonymous

$2^{m} = \frac{ 1 }{ 2^{3}}$

24. anonymous

$a ^{-m} = \frac{ 1 }{ a ^{m} }$

25. anonymous

26. anonymous