Repeated Multiplication

Multiplication is a short way to write repeated addition: $4\cdot 3$ stands for 3 + 3 + 3 + 3. A power does the same job for repeated multiplication. ${2}^{4}$ means four 2s multiplied together: ${2}^{4} = 2\cdot 2\cdot 2\cdot 2$.

The 2 is the base, the number being multiplied. The small raised 4 is the exponent: it counts how many times the base appears. To work out a power, write it out and multiply one pair at a time: $2\cdot 2\cdot 2\cdot 2$, then $4\cdot 2\cdot 2$, then $8\cdot 2$, then 16.

The classic slip is to multiply the base by the exponent. ${2}^{4}$ is not $2\cdot 4$, which is 8. The exponent only counts the factors; it is never one of them.