Indices and Exponents

Section 1What indices mean

An index, or exponent, tells how many times a base is multiplied by itself. In 5³, the base is 5 and the index is 3. In plain words, 5³ means 5 x 5 x 5.

Section 2Main laws

When multiplying powers with the same base, add the indices: a² x a³ = a⁵. When dividing powers with the same base, subtract the indices: a⁵ / a² = a³. Watch out: the base must be the same.

Section 3Power of a power

When a power is raised to another power, multiply the indices. For example, (x²)³ = x⁶. Here's the trick: brackets matter, so read them carefully.

Section 4Fractional exponents

A fractional exponent can show a root. For example, x^(1/2) means the square root of x. Easy to mix up - 9^(1/2) = 3 because 3 x 3 = 9.