# What are exponents?

Power and scientific notation are often used in the laboratory so it is important to familiarise yourself with them.

The power (or exponent) is a number that indicates how many times another number (called the base) is multiplied by itself. For example, 24 is read "two raised to the fourth power" and means that 2 is multiplied by itself 4 times.

Therefore, $2^4 = 2 \times 2 \times 2 \times 2 = 16$

Or another,  $4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024$

The number that is multiplied is called the base and the power to which the base is raised is the exponent. For example, in the expression 103, the base is 10 and the exponent is 3.

Alternatively, a negative exponent indicates that the reciprocal of the number (i.e. one divided by the number) should be multiplied times itself.

For example,

\begin{align*} 1 \div 10^3 &= 10^{-3} \cr &= \frac{1}{10\times 10\times 10} \cr &= \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \cr &= \frac{1}{1000} \cr &= 0.001 \end{align*}

When looking at exponents where the base is 10 (which is the majority of the time in science), there are two general rules to remember:

For numbers greater than 1:

• The exponent or power represents the number of zeros after the number and before the decimal point
• If the exponent or power is positive, the larger the positive exponent, the larger the number.

For example, 1 x 104 = 10,000.0 (notice that there are 4 zeros before the decimal point).

For numbers less than 1:

• The exponent or power represents the number of places to the right of the decimal point including the first non-zero digit
• The exponent or power is negative

For example, 1 x 10-4 = 10-4 = 0.0001 (notice that it is 4 places to the right of the decimal place)