Zero and Negative Exponents - Problem 2
When a fraction is raised to a negative exponent (the entire fraction, that is), follow the basic rules of exponents -- both the numerator and the denominator is raised to that exponent, so "distribute" the exponent to both values. Remember that to simplify a negative exponent, take the reciprocal of the base and change the sign of the exponent. In a fraction, that means the numerator is moved to the denominator and the denominator is moved to the numerator, and the exponents for both are now positive. If the base is an integer, raise the value to the power.
Here I have a fraction or quotient that’s being raised to a negative exponent. Negative exponent means if something were at the top of the fraction, it’s going to become now in the bottom or if something started in the bottom it’s going to become on the top.
So before I do much with this problem I’m going to rewrite this using a positive exponent. I could write this as 2 to the 4th at the bottom of my fraction and then I’ll have 3 to the 4th in the top of my fraction. Like this. Once you guys are able to write out this step, this problem becomes pretty darn easy.
If you want to be a real superstar you can go ahead and do out this multiplication; 3 times 3 is 9 times 3 again is 27 times 3 one more time is 81 on top. On the bottom I’ll have 2 times 2 is 4, times 2 is 8 times 2 is 16. There we go. That’s it. That funny looking thing turned out to that nasty looking fraction and I’m not too worried about how to reduce this or anything because there is no number that multiplies in the 16 that also goes into 81 so that’s my final answer.
When it comes to fractions and negative exponents just be careful that things that started in the bottom are going to move up to the top and things that started in the top are going to move down to the bottom and also make sure your exponent that used to be negative is going to become positive.