SOLUTION: 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 inste

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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