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Rules of powers

When you multiply powers with the same base, you add the exponents. If you divide, you subtract them. A power of a power multiplies the exponents. A number to the power zero is 1, and a negative exponent is 1 divided by the positive power. In standard form you multiply the coefficients separately and the powers of ten separately. If the coefficient becomes 10 or more, you move the decimal point and adjust the exponent.

a^m \cdot a^n = a^{m+n}

product

a^{-n} = \frac{1}{a^n}

negative exponent

(a^m)^n = a^{mn}

power of a power

Symbols

$a$	base
$m,\ n$	exponents

Example

$2^3 \cdot 2^4 = 2^{3+4} = 2^7 = 128$ .

$10^{-2} = 0.01$ .

$(3 \cdot 10^4) \cdot (2 \cdot 10^3) = 6 \cdot 10^7 = 60\,000\,000$ .

Same base: add the exponents. Different bases cannot be combined that way.

Practise powers and standard form for free →

← Standard form · Prefixes →

Part of Mathematics 2P: Powers and standard form.