Hi Mary,

This question bothers me a great deal, it is written to be intentionally confusing. No mathematician or person using mathematics would ever write such an expression. There are rules of precedence, sometimes called BEDMAS that tell you how to proceed but why not write it so the meaning is clear?

The rules of precedence tell you to evaluate anything in parentheses or brackets first. Thus the first step is 8^3/2(2+2) = 8^3/2 * 4 where * is multiplication. There are no parentheses or brackets left so the rules of precedents say to perform any exponents or powers next. In the expression is 8 cubed and 8 cubed is 512 so we have 8^3/2(2+2) = 8^3/2 * 4 = 512/2 * 4. Next in the precedence order is division and 512/2 = 256 so we are left with 8^3/2(2+2) = 8^3/2 * 4 = 512/2 * 4 = 256 * 4 = 1024.

To make clear the order I would have preferred to have the statement written ((8^3)/2)(2+2). The extra parentheses are cumbersome but the meaning is clear. If you are writing this on paper rather than typing it you could write

\[\frac{8^3}{2} \times (2 + 2).\]

Penny