square roots

[Probability]

I am asked to simplify

81^3/4

I did this

4th root 3 x 3 x 3 x 3 = 3^3 = 27

Can somebody explain why it is wrong?

 

[stapel]

I am asked to simplify 81^3/4

Lacking grouping symbols, the above means this:

. . . . .\(\displaystyle \dfrac{81^3}{4}\)

But I think you mean "81^(3/4)", which is this:

. . . . .\(\displaystyle 81^{3/4}\)

4th root 3 x 3 x 3 x 3 = 3^3 = 27

Can somebody explain why it is wrong?

On what basis do you believe that the fourth root of 3^4 is 3^3?

 

[Probability]

Lacking grouping symbols, the above means this:

. . . . .\(\displaystyle \dfrac{81^3}{4}\)

But I think you mean "81^(3/4)", which is this:

. . . . .\(\displaystyle 81^{3/4}\)


On what basis do you believe that the fourth root of 3^4 is 3^3?

I am trying to learn this from first principles and I only have the examples in my course book to follow, which are all presented the way I have presented this example, so I am trying to get to the understanding of what is meant by the 4th root?

I am also to understand that

\(\displaystyle 81^[3/4]\) => (sqrt root 3x3x3x3)^3 = 3^3 = 27

My coursework does not show this but was given by a tutor. I am still not getting the understanding though?

 

[HallsofIvy]

I am asked to simplify

81^3/4

I did this

4th root 3 x 3 x 3 x 3 = 3^3 = 27

Can somebody explain why it is wrong?

Assuming you mean 81 to the 3/4 power (better written 81^(3/4). 81^3/4 really means (81^3)/4.)
that is the correct answer but you have written your solution badly. The fourth root of 81 is the "fourth root of 3 x 3 x 3 x 3" and that is equal to 3. The third power of that is 3^3= 27.

But "4th root 3 x 3 x 3 x 3" is NOT equal to 3^3.