Question 282874
120 - 3^3 * 4 ÷ 6 + 7

This is a typical problem concerning the Order of Operations, abbreviated PEMDAS, standing for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".  An easy way to remember this is with the mnemonic "Please Excuse My Dear Aunt Sally". Always perform operations in sequence and, for operations with the same priority (multiplication & division) and (addition & subtraction) work from left to right.

In your example of 
120 - 3^3 · 4 ÷ 6 + 7
We have no parentheses, so the first thing we need to do is evaluate the exponent 3^3, which, of course is the same as 3 * 3 * 3 = 27.  Now our problem reads: 
120 - 27 * 4 ÷ 6 + 7
Starting from the left again, our highest priority is the multiplication of 27 * 4, which = 108, giving us:
120 - 108 ÷ 6 + 7
Our next operation is division of 108 / 6 = 18
120 - 18 + 7
120 - 18 = 102 then add 7 giving us a total of 109 and bobs your uncle.  :)