SOLUTION: How would I evaluate an expression with a mixed-number exponent, such as 8 to the one and one-third power?

Question 83822: How would I evaluate an expression with a mixed-number exponent, such as 8 to the one and one-third power?
Found 2 solutions by josmiceli, Earlsdon:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
There are two ways. 1 1/3 is actually 1 + 1/3, so you'd have

Use the rule

The cube root of 8 is 2

answer
The other way is 1 1/3 = 4/3

Note that 4/3 is actually
Use the rule

same answer
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Evaluate 8 raised to the 1 1/3 power.
First, change the exponent to an improper fraction so that it looks like:
...and this is read as...the cube root of 8 to the fourth power.
Find 8 to the fourth power: (8*8*8*8 = 64*64 = 4096)
Now find the cube root of 4096...and this = 16 (4096 = 16*16*16)
So, 8 raised to the 1 1/3 power = 16.
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