Expert: Josh - 8/26/2009

Question
Im doing my best but I still dont understan the following :
2[(8-4)+3(6-3)^2]^0-[4(6)^-3]^2-10(50)^0=

Answer
Rebecca,

The bits and pieces inside the square brackets are the first things we should concentrate on. Although it makes little difference in this example, we should work from left to right when we simplify expressions as a general rule.

For the first square bracket:
(8-4)=4

When dealing with 3(6-3)^2, we first simplify what is inside the round brackets. So, 3(6-3)^2 becomes 3*(3)^2. At this stage, remember that the exponent has higher associative power with the base (3) than the left hand side multiplication. So, we attend to the squaring first. 3*(3)^2 becomes 3*(3*3) = 3(9). Finally, a straight forward multiplication gives 27.

So, incorporating the simplifications for the first square bracket, the overall expression becomes
2 [4+27]^0 - [4(6)^-3]^2 - 10(50)^0

For the second square bracket:

4(6)^-3 is simplified in the same way. As the exponent has higher associative power with the base (6) than the left hand side multiplication, we attend to it first. 4*(6)^-3 becomes 4*(1/(6*6*6)) = 4/216 = 1/54. We have use the fact that a^(-b) = 1/[a^b].

The overall expression becomes
2 [4+27]^0 - [1/54]^2 - 10(50)^0  ...[1]

Now, by definition, x^0 for any number x is equal to 1. So, [1] becomes

2*1 - 1/(54)^2 - 10*1
= -8 -1/(54)^2