SOLUTION: Hi! My math teacher wants an example problem that can be solved applying three different laws of exponents. We must list the laws that we use and solve the problem. Thank you so m

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi! My math teacher wants an example problem that can be solved applying three different laws of exponents. We must list the laws that we use and solve the problem. Thank you so m      Log On


   

Question 450872: Hi!
My math teacher wants an example problem that can be solved applying three different laws of exponents. We must list the laws that we use and solve the problem. Thank you so much for your time!!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Solved Example using 3 of Exponent Rules


Simplify %28x%5E%281%2F3%29+-+x%5E%28-1%2F3%29%29%28x%5E%282%2F3%29+%2B+1+%2B+x%5E%28-2%2F3%29%29


Let A+=+%28x%5E%281%2F3%29+-+x%5E%28-1%2F3%29%29%28x%5E%282%2F3%29+%2B+1+%2B+x%5E%28-2%2F3%29%29


We know


Similarly, x%5E%28-2%2F3%29+=+%28x%5E%28-1%2F3%29%29%5E2


If we denote x%5E%281%2F3%29 by a, and x%5E%28-1%2F3+%29by b,


then ab+=+x%5E%281%2F3%29+%2A+x%5E%28-1%2F3%29+=+1 [Since pn and p-n are reciprocals to one another.]


Thus A becomes %28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29.


We know %28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29+=+a%5E3+-+b%5E3


so, +A+=+a%5E3+-+b%5E3+=+%28x%5E%281%2F3%29%29%5E3+-+%28x%5E%28-1%2F3%29%29%5E3



= ....this is your answer