Powers, Bases and Exponents

≈ 20 min

A power is a short way to write repeated multiplication. In $5^3$ , the big number $5$ is the base and the small number $3$ is the exponent (or index). The exponent tells you how many times to multiply the base by itself:

5^3 = 5 \times 5 \times 5 = 125

We read this as "5 to the power of 3" or "5 cubed". Note carefully that $5^3$ is not $5 \times 3$ — the exponent counts factors, it is not itself a factor.

Worked example. Evaluate $2^4$ .

2^4 = 2 \times 2 \times 2 \times 2 = 16

Build it up left to right: $2 \times 2 = 4$ , then $4 \times 2 = 8$ , then $8 \times 2 = 16$ .

What does $2^5$ mean?

$2 \times 5$

$2 \times 2 \times 2 \times 2 \times 2$

$5 \times 5$

$5^2$

Evaluate $3^4$ .

Evaluate $2^6$ .

A learner writes $6^2 = 12$ . Which statement is correct?

$6^2 = 12$ ; the working is right

$6^2 = 36$ ; they multiplied the base by the exponent instead of squaring

$6^2 = 8$ ; they added 6 and 2

$6^2 = 12$ ; a power always means base times exponent