Order of operations, powers and roots.

Step 1 of 6

What comes first?

An expression such as $2 + 3 \times 4$⁠ has two operations, and the answer depends on which one you work out first. So that everyone gets the same answer, there is a convention:

1. Brackets first, from the innermost outward.
2. Powers and roots.
3. Multiplication and division, from left to right.
4. Addition and subtraction, from left to right.

The board shows the expression, and Look inside works it out line by line, naming in each line the rule that chose the operation. Predict the answer first.

Step 2 of 6

Brackets

Brackets change the usual order: what is inside them is worked out before anything else. Answer, then drag Look inside to see the lines of working. Then try other numbers with a, b and c.

Step 3 of 6

Powers

A power is a number multiplied by itself again and again: $4^2 = 4 \times 4 = 16$$4^2 =$$4 \times 4 =$$16$⁠ and $2^3 = 2 \times 2 \times 2 = 8$$2^3 =$$2 \times 2 \times 2 =$$8$⁠. The exponent, the small number at the top, says how many times. Powers are worked out before multiplication, and a power applies only to the number right under it.

Step 4 of 6

Squares

$6^2$⁠ is called “six squared”, because it is the number of cells in a square of side $6$⁠. Answer, then drag Look inside to count the cells.

Step 5 of 6

Roots

The square root is the inverse operation: $\sqrt{36}$⁠ is the side of a square of area $36$⁠, that is $6$⁠, because $6^2 = 36$⁠. The root sign works like brackets: what is under it is worked out first.

Step 6 of 6

Minus, squared

A power also comes before a minus sign in front of a number. Predict the result, then watch the working.