SOLUTION: can you show me how to work the problem: 12 with an exponent of 3/4 divided by 5 with an exponent of 1/3. If you can tell me how to use a calculator to do it also would be of gre

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: can you show me how to work the problem: 12 with an exponent of 3/4 divided by 5 with an exponent of 1/3. If you can tell me how to use a calculator to do it also would be of gre      Log On


   

Question 759904: can you show me how to work the problem: 12 with an exponent of 3/4 divided by 5 with an exponent of 1/3. If you can tell me how to use a calculator to do it
also would be of great help.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
can you show me how to work the problem: 12 with an exponent of 3/4 divided by 5 with an exponent of 1/3. If you can tell me how to use a calculator to do it
also would be of great help.

First the exact value as a rationalized root:

matrix%282%2C1%2C%22%22%2C12%5E%283%2F4%29%2F5%5E%281%2F3%29%29

Get the two fraction exponents with a common denominator of 12

3%2F4=9%2F12, 1%2F3=4%2F12

matrix%282%2C1%2C%22%22%2C12%5E%289%2F12%29%2F5%5E%284%2F12%29%29

root%2812%2C12%5E9%29%2Froot%2812%2C5%5E4%29

root%2812%2C12%5E9%29%2Froot%2812%2C5%5E4%29%22%22%2A%22%22root%2812%2C5%5E8%29%2Froot%2812%2C5%5E8%29

root%2812%2C12%5E9%2A5%5E8%29%2Froot%2812%2C5%5E12%29

root%2812%2C12%5E9%2A5%5E8%29%2F5

root%2812%2C2015539200000000%29%2F5, that's the exact value.

As a decimal approximation 3.77047385

On a calculator, 

(12^(3/4))/(5^(1/3))

Get the decimal approximation 3.77047385

Edwin