SOLUTION: How do I evaluate 8^-4/3? I am having difficulty understanding how to evaluate an exponent when it is both fractional and negative.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: How do I evaluate 8^-4/3? I am having difficulty understanding how to evaluate an exponent when it is both fractional and negative.      Log On


   

Question 705260: How do I evaluate 8^-4/3? I am having difficulty understanding how to evaluate an exponent when it is both fractional and negative.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%282%2C1%2C%0D%0A%22%22%2C%0D%0A8%5E%28-4%2F3%29%29

Change 8 to 2³

matrix%282%2C1%2C%0D%0A%22%22%2C%0D%0A%282%5E3%29%5E%28-4%2F3%29%29

Multiply exponents

matrix%282%2C1%2C%0D%0A%22%22%2C%0D%0A2%5E%28++3%28++expr%28-4%2F3%29++%29%29+%29

Cancel the 3's in the exponent



So we have

matrix%282%2C1%2C%0D%0A%22%22%2C%0D%0A2%5E%28-4%29+%29

Bring negative exponent to the denominator as a positive exponent

1%2F2%5E4

1%2F16

Edwin