Question:
What is the difference between the following problems:

(-5)², -5² and -(5)²

Our text book (Beginning Algebra, fourth edition, published by McGraw Hill, by Streeter, Huthison and Hoetzle) says the second and third problem are exactly the same. I don't see how that can be. Is there a mathematical rule that explains this?

Hi Jennifer,

The parentheses in the first and third expression make it clear which part of the expression is raised to the power 2. In the first expression the power of 2 applies to -5 hence

In the third expression the parentheses tell us that the power of 2 applies to 5 and hence

For the second expression, without the parentheses, we use the rules of precedence which tell us which operations to perform first. This convention is to first perform any exponentiation (powers), then any divisions and multiplications and lastly any + or - operations. Some people use memory devices to remember this convention, one of which is PEDMAS (Parentheses, Exponentiation, Division, Multiplication, Addition then Subtraction). In your problem -5² first apply the exponentiation and then the negation, hence

Cheers,
Penny