# 2.7 Powers and roots

There are several **symbols for powers and roots**: for instance, 2^{4} means ‘2 to the power 4’. An alternative to 2^{4} is 24, where the symbol means ‘to the power’. This symbol is often used by computers and calculators.

A related symbol is the square root symbol, as in meaning the positive square root of 25 (that is, 5). Symbols for other roots, are exemplified by meaning the cube root of 8 (that is, 2).

Raising to the power ^{−}1 gives the symbol for a reciprocal: thus, 6^{−1} means the reciprocal of 6, or . The symbols used by calculators for scientific notation often involve the letter E: for example, 3.1E2 means 3.1 × 10^{2}, or 310.

## Example 5

What do the following expressions mean?

(a) 5

^{2}(b)

(c) (5 + 8)

^{2}(d) 2

^{−1}(e)

### Answer

(a) Square 5. (This gives 25.)

(b) Positive square root of 100 (This gives 10.)

(c) Add 5 and 8, and then square the result. (This gives 169.)

(d) The reciprocal of 2. (This gives or 0.5.)

(e) The square root of the sum of 10 and 6. (That is, 4.)