SOLUTION: SIMPLIFY THE EXPRESSION. (3x^4)^3/x^15 Please explain each step. Thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: SIMPLIFY THE EXPRESSION. (3x^4)^3/x^15 Please explain each step. Thank you!      Log On


   

Question 611063: SIMPLIFY THE EXPRESSION.
(3x^4)^3/x^15
Please explain each step. Thank you!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E4%29%5E3%2Fx%5E15
According to the order of operations (aka PEMDAS), exponents come before multiplying or dividing. So we start in the numerator. Using the rule for exponents, %28a%2Ab%29%5Eq+=+a%5Eq%2Ab%5Eq, on %283x%5E4%29%5E3 we get:
%283%5E3%2A%28x%5E4%29%5E3%29%2Fx%5E15
Using the rule for exponents, %28a%5Eq%29%5Ep+=+a%5E%28q%2Ap%29, on %28x%5E4%29%5E3 and since 3%5E3+=+27 we get:
%2827x%5E12%29%2Fx%5E15
Next we use another rule for exponents, a%5Eq%2Fa%5Ep+=+a%5E%28q-p%29, on x%5E12%2Fx%5E15 we get:
27x%5E%28-3%29
This may be an acceptable answer. If you don't want a negative exponent, then we can replace x%5E%28-3%29 with 1%2Fx%5E3
27%281%2Fx%5E3%29
which simplifies to
27%2Fx%5E3