Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

yes

Answer 5

Into factors of the number.

Answer 6

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

Answer 7

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

Answer 8

So
\[x ^{12}=(x ^{4})^{3}=(x ^{6})^{2}\]

Answer 9

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.

Answer 10

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

Answer 11

3(1/2)=3/2

Answer 12

\[3(\frac{1}{2})=\frac{3}{2}\]

Answer 13

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?

Answer 14

No. It's always multiplication.

Answer 15

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. =(

Answer 16

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.

Answer 17

it is 3*1/2

Answer 18

\[(\frac{3}{1})(\frac{1}{2})=\frac{(3)(1)}{(1)(2)}=\frac{3}{2}\]

Answer 19

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?

Answer 20

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.

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

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?

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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.

Answer 29

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)?

Answer 30

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

Answer 31

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!

Answer 32

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

Answer 33

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