Order of Operations

In Algebra, the Order of Operations is the sequence to be taken in solving or simplifying equations.

In its simplest form, the order is: It gets a little more complicated when the problem contains brackets or parentheses, as we must first apply the same order to math inside them before working on the math outside of them.
 * 1) Raising exponents to their powers and extracting roots in the order that you come to them in the problem.
 * 2) Multiplying and dividing in the order that you come to them in the problem.
 * 3) Adding and subtracting in the order that you come to them in the problem.

Examples
Applying the Order of Operations, we would simplify the following expression like this: $$2^3 + 6 * 4 - \scriptstyle \sqrt{16} + \tfrac{10}{5}$$ $$8 + 6 * 4 - 4 + \tfrac{10}{5}$$ $$8 + 24 - 4 + 2$$ $$30$$
 * First, we do the exponents and extra the roots
 * Next, we do multiplication and division
 * Finally, we do addition and subtraction

Let's bring the expression above into a new example with parentheses: $$3^3 * 2 - (2^3 + 6 * 4 - \scriptstyle \sqrt{16} + \tfrac{10}{5}) - (4 + 2^3) * 6$$ $$3^3 * 2 - (8 + 6 * 4 - 4 + \tfrac{10}{5}) - (4 + 8) * 6$$ $$3^3 * 2 - (8 + 24 - 4 + 2) - (4 + 8) * 6$$ $$3^3 * 2 - (30) - (12) * 6$$ $$27 * 2 - 30 - 12 * 6$$ $$54 - 30 - 72$$ $$-48$$
 * First, we do exponents and extract roots within the parentheses.
 * Next, we do multiplication and division within the parentheses.
 * Then, we do addition and subtraction within the parentheses.
 * Now that the parentheses are finished, we do the same thing step by step in the rest of the problem. Exponents & roots:
 * Multiplication & division:
 * Addition & substraction: