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## anonymous 4 years ago I know this may be a simple question but how does 9^3/2 = (9^1/2)^3? I'm not very math literate.

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1. Mertsj

When you raise something to a power, you multiply the exponents. For example x^4 could be written( x^2)^2 because 2 times 2 is 4.

2. Mertsj

So in your example, since 1/2 times 3 = 3/2 those expressions are the same.

3. anonymous

Hey Mertsj, thank you for your reply. =) So basically you can just split up the components that make up this expression?

4. Mertsj

yes

5. Mertsj

Into factors of the number.

6. anonymous

and 'factors' are just like the " (x^2)^2 " of x^4?

7. Mertsj

factors are numbers that you multiply. The factors of 12 are 4 and 3 because 4 times 3 = 12

8. Mertsj

So $x ^{12}=(x ^{4})^{3}=(x ^{6})^{2}$

9. anonymous

So in my example, 3/2. When you raise 1/2 to the third power is it like 1/2 + 1/2 + 1/2 or, 1/2 * 1/2 * 1/2? If I multiply 3 times 1/2 I get 1/2.

10. Mertsj

It is like 1/2+1/2+1/2 NOT 1/2*1/2*1/2 because that would be 1/8

11. Mertsj

3(1/2)=3/2

12. Mertsj

$3(\frac{1}{2})=\frac{3}{2}$

13. anonymous

Yup, its 1/8. So x^12 = (x^4)^3 = (x^6)^2 that like, 4*3 which equals 12 although when dealing with fractional exponents, its addition?

14. Mertsj

No. It's always multiplication.

15. anonymous

3(1/2) is 1/2*1/2*1/2 which equals1/8. My bad, I think its actually 3/1*1/2. I am so terrible at math. =(

16. anonymous

I think its actually 3/1 * 1/2. You can convert any whole number to a fraction by adding a '1' underneath it I believe.

17. Mertsj

it is 3*1/2

18. Mertsj

$(\frac{3}{1})(\frac{1}{2})=\frac{(3)(1)}{(1)(2)}=\frac{3}{2}$

19. anonymous

Thank you for your help. =) It has clarified my confusion. I just have one last question, why would you go through the hassle of converting 9^3/2 to (9^1/2)^3? Is it because you couldn't get the actual root of 9 with 3/2?

20. Mertsj

For the simple reason of giving you practice with the idea of multiplying exponents when raising to a power. You probably would not actually do that very often unless you were trying to factor an expression that has fractions for exponents.

21. anonymous

So how would you actually break down 9^3/2 to 3^3 in steps without using (9^1/2)^3?

22. Mertsj

For example: $x ^{\frac{1}{2}}+x ^{\frac{3}{2}}=x ^{\frac{1}{2}}(1+x ^{1})$

23. Mertsj

When you have a fractional exponent, remember that the bottom number of the fraction tells you the root and the top number tells you the power.

24. anonymous

I think I get it, 8^2/3 would be 2^2? This confused me by the way. x^1/2 + x^3/2 = x^1/2(1 + x^1) Wouldn't that be x^4/2?

25. Mertsj

So: $9^{\frac{3}{2}}=(\sqrt{9})^{3}=(3)^{3}=27$

26. Mertsj

No. When you multiply, you add the exponents and only like terms can be added.

27. Mertsj

And yes, 8^2/3 = 2^2 or 4

28. anonymous

I'm still trying to understand this, x^1/2 + x^3/2 = x^1/2(1 + x^1) Its making my brain hurt. =P What do you mean, you add the exponents and only like terms can be added. Yi yi, I'm very sorry.

29. anonymous

Wouldn't you distribute x^1/2 to the numbers inside the parentheses of x^1/2 + x^3/2 = x^1/2(1 + x^1)?

30. Mertsj

Yes. And in doing so, you would add the exponents. So you would have x^1/2(1) which is x^1/2 and then x^1/2(x^1)=x^1/2(x^2/2)=x^3/2

31. anonymous

I keep thinking on x^1/2 + x^3/2, you would add the exponents but that is fractions I believe. A whole other story!

32. Mertsj

$x ^{\frac{1}{2}}(1+x ^{1})=x ^{\frac{1}{2}}(1+x ^{\frac{2}{2}})=x ^{\frac{1}{2}}(1)+x ^{\frac{1}{2}}(x ^{\frac{2}{2}})$

33. Mertsj

And $x ^{\frac{1}{2}}(x ^{\frac{2}{2}})=x ^{\frac{1}{2}+\frac{2}{2}}=x ^{\frac{3}{2}}$

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