power

The power of a number tells us how many times to multiply that number by itself.

It’s written as a small number to the right of the base and higher than it.

For example, we write the second power of 10 as 102, which is 10 × 10 = 100. We say 102 as ’10 to the power 2′.

This pattern can be continued, for example the third power of 10 which is written as 103. This is 10 × 10 × 10 = 1000.

The powers of other numbers are defined in the same way. For example the powers of 2:

    22, which is 2 × 2 = 4
    23, which is 2 × 2 × 2 = 8
    24, which is 2 × 2 × 2 × 2 = 16

Power can also be fractional. A fractional power represents a root:

    x^\frac{1}{2}=\sqrt{x}

For example, 9^\frac{1}{2} would be \sqrt{9} = \textmd 3.

Power can also be negative. A negative power represents a reciprocal:

    x^{-1}=\dfrac{1}{x}

For example, 2-1 would be \dfrac{1}{2}.

Any number or variable to the power 0 is equal to 1:

    x^{0}={1}

For example, 50 would be 1.