SOLUTION: How do you simplify this question?? Use the properties of exponents to simplify the seemingly unsimplifiable: 486(power 38) Over 3(power 187) Your final answer should be

Algebra ->  Test -> SOLUTION: How do you simplify this question?? Use the properties of exponents to simplify the seemingly unsimplifiable: 486(power 38) Over 3(power 187) Your final answer should be       Log On


   

Question 504861: How do you simplify this question??
Use the properties of exponents to simplify the seemingly unsimplifiable:
486(power 38)
Over
3(power 187)
Your final answer should be in scientific notation
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
486 = 3^5 * 2
your equation of:
486^(38) / 3^187 becomes:
(3^5*2)^38 / 3^187 which becomes:
(3^(5*38)*2^38) / 3^187 which becomes:
3^190*2^38 / 3^187 which becomes:
3^(190-187)*2^38 which becomes:
3^3 * 2^38 which becomes:
7.42170349 * 10^12
here's a picture of how it would look if done by hand.
$$$$$
the key was in getting the numerator to have a base of 3.
successive divisions of 486 by 3 yielded 5 divisions yielding a last factor of 2.
that led to 486 = 3^5*2
from there on it was laws of exponents all the way.
x^a * x^b = x^(a+b)
(x^a)^b = x^(a*b)
x^a/x^b = x^(a-b)