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

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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) About Me  (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
8%5E%281%2B%281%2F3%29%29
Use the rule x%5E%28a%2Bb%29+=+%28x%5Ea%29%28x%5Eb%29
8%5E%281%2B%281%2F3%29%29+=+%288%5E1%29%288%5E%281%2F3%29%29
The cube root of 8 is 2
8%5E%281%2B%281%2F3%29%29+=+8%2A2
8%2A2+=+16 answer
The other way is 1 1/3 = 4/3
8%5E%281%2B%281%2F3%29%29+=+8%5E%284%2F3%29
Note that 4/3 is actually 4%2A%281%2F3%29
Use the rule x%5E%28a%2Ab%29+=+%28x%5Ea%29%5Eb
8%5E%284%2F3%29+=+%288%5E%281%2F3%29%29%5E4
8%5E%284%2F3%29+=+2%5E4
8%5E%284%2F3%29+=+16 same answer

Answer by Earlsdon(6294) About Me  (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:
8%5E%284%2F3%29...and this is read as...the cube root of 8 to the fourth power.
Find 8 to the fourth power:8%5E4+=+4096 (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.