# Exponents

#### CSmith

##### Member
32 2/5(on top of the 32)+64 2/3(on top of the 64. I got 7

(32 1/5 on top)squared =5
(64 2/3=(64 1/3) squared (2)=96 squared=2

#### Jameson

Staff member
32 2/5(on top of the 32)+64 2/3(on top of the 64. I got 7
What did you get for each term? There are two terms added together in this problem so doing each part separately will help us understand your thought process.

#### CSmith

##### Member
What did you get for each term? There are two terms added together in this problem so doing each part separately will help us understand your thought process.
ok for the first part this is what i did

1.)(32 1/5)2(squared = 32 to the 5th power(

32x5=160 so i have to find the power to give me 160 which is 32x5. so 32x32x32x32x32=5 .i got 5 for that.

2nd part 2.) 64 2/3=(64 1/3)squared....64x3=192.then i have to ask what power gives me 192. and i got 96 squared.96x96 gives me my 192 so i put the power which is =2

5+2=7

#### Jameson

Staff member
ok for the first part this is what i did

1.)(32 1/5)2(squared = 32 to the 5th power(

32x5=160 so i have to find the power to give me 160 which is 32x5. so 32x32x32x32x32=5 .i got 5 for that.

2nd part 2.) 64 2/3=(64 1/3)squared....64x3=192.then i have to ask what power gives me 192. and i got 96 squared.96x96 gives me my 192 so i put the power which is =2

5+2=7
You start with $$\displaystyle 32^{\frac{2}{5}}$$. The 2 means square 32 and the $$\displaystyle \frac{1}{5}$$ or 5 in the bottom means find a number which multiplied by itself 5 times equals 32.

Your first idea was good. You tried to find $$\displaystyle 32^{\frac{1}{5}}$$. To do that you need to find a number that when multiplied by itself 5 times equals 32, not that number times 5. Start with really small numbers and multiply them together 5 times. You should quickly figure that out.

Put another way, $$\displaystyle x^5 = x \cdot x \cdot x \cdot x \cdot x$$ not $$\displaystyle 5x$$

#### CSmith

##### Member
i squared the 32 and got 1024

#### Sudharaka

##### Well-known member
MHB Math Helper
i squared the 32 and got 1024
Hi CSmith,

Yes it's correct. You can do this problem in two ways.

1) Find $$32^{\frac{1}{5}}$$ first and then square the answer to find $$32^{\frac{2}{5}}$$.

2) Find $$32^{2}$$ first and then take the fifth root. You have done the first part. Now what remains is to find a number $$x$$ such that, $$32^{2}=1024=x^5$$. Then $$x=32^{\frac{2}{5}}$$

Among these methods I think it would be easier to use the first method since $$32^{\frac{1}{5}}$$ is easier to find than, $$1024^{\frac{1}{5}}$$

Kind Regards,
Sudharaka.

#### CSmith

##### Member
Thanks! after that what should i do?

Hi CSmith,

Yes it's correct. You can do this problem in two ways.

1) Find $$32^{\frac{1}{5}}$$ first and then square the answer to find $$32^{\frac{2}{5}}$$.

2) Find $$32^{2}$$ first and then take the fifth root. You have done the first part. Now what remains is to find a number $$x$$ such that, $$32^{2}=1024=x^5$$. Then $$x=32^{\frac{2}{5}}$$

Among these methods I think it would be easier to use the first method since $$32^{\frac{1}{5}}$$ is easier to find than, $$1024^{\frac{1}{5}}$$

Kind Regards,
Sudharaka.

#### CSmith

##### Member
can u show me an easiert method to do this sum please

#### Sudharaka

##### Well-known member
MHB Math Helper
Thanks! after that what should i do?
can u show me an easiert method to do this sum please
I suggest that you review how to simplify fractional exponents and try to find the answer to your question along the methods described above. Some useful webpages are given below,