1.2 Learn Basic Properties and Operations

In algebraic expressions and equations, we often see numbers or variables raised to a power. The power is represented by an exponent, a small number written above and to the right of a base.

In the example below, 6 is the base and 3 is the exponent. The base tells the factor to be multiplied. The exponent tells how many times the base appears in the multiplication problem.

Example

$${6^3} = 6 \times 6 \times 6 = 216$$

Since the powers 2 and 3 are often used, we have special words for them. A number raised to the second power is said to be “squared.”

Example

“5 squared” means $${5^2}$$, which equals $$5 \times 5 = 25$$

A number raised to the third power is said to be “cubed.”

Example

“4 cubed” means $${4^3}$$, which equals $$4 \times 4 \times 4 = 64$$

Some students make the mistake of thinking that squaring a number is the same as doubling it. It isn’t. Doubling a number multiplies the number by 2. (10 doubled equals 20.) Squaring a number multiplies that number by itself: $${10^2} = 100$$.