# exponent

#### CSmith

##### Member
1.) 8 3/2

=(81/2)3
=(2 squareroot 8)2

(2 square root 2x2x2)3

=(2 square root )3
=2 square root x 2 square root x 2 square root=8 (2 square root)
=16 square root 2

#### Jameson

Staff member
1.) 8 3/2

=(81/2)3
=(2 squareroot 8)2

(2 square root 2x2x2)3

=(2 square root )3
=2 square root x 2 square root x 2 square root=8 (2 square root)
=16 square root 2

#### CSmith

##### Member
Thanks! im trying...

#### CSmith

##### Member
how do i know when the answer should be in square root form like 16 square root 2 or when it is suppose to be in powers like my answer for 32 2/5 when the answer was 2^2.

#### Jameson

Staff member
how do i know when the answer should be in square root form like 16 square root 2 or when it is suppose to be in powers like my answer for 32 2/5 when the answer was 2^2.
The final answer to that problem is 4. There's no reason to write it as 2^2.

With square roots, you simplify as much as you can until you are left with a prime number, so you must keep the square root sign or use a decimal approximation, which is not preferred. If you have something like $$\displaystyle \sqrt{20}$$ then you can simplify it but there will be a square root in the final answer.

Last edited:

#### Ackbach

##### Indicium Physicus
Staff member
The final answer to that problem is 4. There's no reason to write it as 2^2.

With square roots, you simplify as much as you can until you are left with a prime number, so you must keep the square root sign or use a decimal approximation, which is not preferred. If you have something like $$\displaystyle \sqrt{20}$$ then you can simplify it but there will be a square root in the final answer.
True so far as it goes. An engineering professor is not necessarily going to want a highly complicated but exact answer when an easy-to-understand decimal approximation helps the bridge get built more easily.