## anonymous 5 years ago 2 raised to the power of 5/2 - 2 raised to the power of 3/2

1. anonymous

When you raise a power to a power you multiply the exponents.

2. anonymous

well my answers are either A. 2 1/2 B. 2 C. 2 3/2 D. 2 5/3 or E. 2^2

3. anonymous

Well, what is (5/2-2)(3/2)

4. anonymous

3/4?

5. anonymous

$(2^{\frac{5}{2}-2})^{\frac{3}{2}}$ $= 2^{\frac{3}{2}(\frac{5}{2}-2)}$ $= 2^{\frac{3}{2}\frac{5}{2} - \frac{3}{2}\frac{2}{1}}$ $= 2^{\frac{15}{4} - \frac{12}{4}}$ $= 2^{\frac{3}{4}}$

6. anonymous

Wait. I think you have a different problem.

7. anonymous

thats not one of the answers ,the question is 2 raised to 5 over 2 subtract 2 raised to 3 over 2?

8. anonymous

Yeah, you should put parens on that.. Do you mean $2^{\frac{5}{2}} - 2^{\frac{3}{2}}$

9. anonymous

yes

10. anonymous

Very different problem ;p

11. anonymous

You can factor a 1/2 from the exponents.

12. anonymous

Actually no you cannot.

13. anonymous

That's just $$\sqrt{32} - \sqrt{8}$$

14. anonymous

if i do 2 5/2 divided by half i get 9 and if i do 2 3/2 divided by half i get 7 so if i subtract them i obviously get 2 which is b but i dont think thats right

15. anonymous

$$\sqrt{32} = \sqrt{2^2*2^2*2} = 2*2\sqrt{2} = 4\sqrt{2}$$

16. anonymous

the answer is 2 and 3/2 but i dont no how they got that

17. anonymous

$$\sqrt{8} = \sqrt{2^2*2} = 2\sqrt{2}$$ $\implies \sqrt{32} - \sqrt{8} = 4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}$ So the answer should be $$2^{\frac{3}{2}}$$

18. anonymous

where are you getting the square roots from

19. anonymous

$$2^{\frac{1}{2}} = \sqrt{2}$$

20. anonymous

im so confused

21. anonymous

Well think about it this way then.

22. anonymous

Multiplying powers of the same base you add their exponents. $$2^{5/2}$$ $$= 2^{4/2} \bullet 2^{1/2}$$ $$=2^2 \bullet 2^{1/2}$$ $$= 4(2^{1/2})$$

23. anonymous

Same for $$2^{3/2} = 2(2^{1/2})$$

24. anonymous

So $$4(2^{1/2}) - 2(2^{1/2}) = 2(2^{1/2})$$

25. anonymous

$$= 2^1* 2^{1/2} = 2^{1+1/2} = 2^{3/2}$$

26. anonymous

so i just add 5/2 + 3/2?

27. anonymous

no. Watch this series on exponents.. http://www.khanacademy.org/video/exponent-properties-1?playlist=Developmental%20Math

28. anonymous

haha i did but i dont get subtraction... with exponents

29. anonymous

That's because you can't do anything special when you are adding and subtracting exponents. You can only factor out common factors. But in this case you have a common factor of 2^{1/2} that you can pull out of each term.