Exponents give us a new way to describe operations with numbers, so we need to understand how exponents work with other operations.

When we write an expression such as $6 \boldcdot 4^2$, we want to make sure everyone agrees about how to find its value. Otherwise, some people might multiply first and others compute the exponent first, and different people would get different values for the same expression!

Earlier we saw situations in which $6 \boldcdot 4^2$ represented the surface area of a cube with edge lengths of 4 units. When computing the surface area, we compute $4^2$ first (or find the area of one face of the cube first) and then multiply the result by 6 (because the cube has 6 faces).

In many other expressions that use exponents, the part with an exponent is intended to be computed first.

To make everyone agree about the value of expressions like $6 \boldcdot 4^2$, we follow the convention to find the value of the part of the expression with the exponent first. Here are a couple of examples:

If we want to communicate that 6 and 4 should be multiplied first and then squared, then we can use parentheses to group parts of the expression together:

In general, to find the value of expressions, we use this order of operations:

• Do any operations in parentheses.
• Apply any exponents.
• Multiply or divide from left to right in the expression.
• Add or subtract from left to right in the expression.