Raising Powers

If you multiply a number by four, you add the original number to \(0\) four times.

When you raise a number to the \(n\)th power, you multiply \(1\) by the number four times.

We write \(b^n\), and say “\(b\) to the power \(m\)”. This way of writing is known as index notation.

\[b^n = \underbrace{b \times b \times b \times \dotsb \times b}_n.\]

Squares

Squaring a number means multiplying itself by itself, so the square of \(x\) is \(x^2\) and we say “\(x\) squared”.

It’s useful to see that any number, when squared, will always be positive or zero.

Cubes

Similarly, cubing raises a number to the power of three.

Naming This Operation

Just as multiplying is called multiplication, raising a number to a power is called exponentiation.