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Question 1105691: Please help me solve the monomial -2^8 times 5^3 over 5^4 times 2^10 times 10
The problem asks me to calculate but my teacher taught us an easier way of solving the monomial instead of simplifying and multiplying every expression but i just forgot how
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! not sure what your teacher taught you, but here's a way that i learned from online tutorials.
(-2^8 * 5^3) / (5^4 * 2^10 * 10) equals:
-1/10 * 2^8/2^10 * 5^3/5^4 equals:
-1/10 * 2^(8-10) * 5^(3-4) equals:
-1/10 * 2^(-2) * 5^(-1) equals:
-1/10 * 1/2^2 * 1/5^1 equals:
-1/10 * 1/4 * 1/5 equals:
-1/10 * 1/20 equals:
-1/200.
note that -2^8 is not the same as (-2)^8.
-2^8 is the same as -(2^8).
if they showed it to you without the parentheses surrounding the -2, then it -(2^8).
the concepts involved are:
x^a / x^b is equal to x^(a-b).
x^(-a) is equal to 1/x^a.
-x^a is equal to -1 * x^a which is equal to -(x^a)
(-x)^a is equal to (-x)^a
also some more exponential arithmetic properties.
(x*y)^a is equal to x^a * y^a
(x/y)^a is equal to x^a / y^a
these properties, and possibly more, are covered in tutorials 42 to 48 in the following reference.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm
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