NUMBAT OER - Open Educational Resources

4. Powers of powers

In the last section, we multiplied powers of ten (or numbers expressed as a figure multiplied by a power of ten) by adding the powers together. How do we deal with a situation where we want to evaluate an expression where a number expressed as a power of ten is itself raised to a power? For instance, what is the square of one billion?

1 000 000 000 × 1 000 000 000 = 1 000 000 000 000 000 000

Written in power notation, this becomes:

(109)2 = 1018

Notice that the superscript of the answer is the product (not the sum) of the superscripts of the expression to the left of the equals sign. Similarly, we can raise to a power a number expressed in scientific notation:

(5 × 107)3 = 53 × (107)3 = 53 × 1021 = 1.25 × 1022