Fractions, powers, roots

The quotient a/b of two integers with b not zero: the number which, multiplied by b, gives a. It is in lowest terms when a and b share no divisor other than 1.

To add, you first need a common denominator: 1/4 + 1/6 = 3/12 + 2/12 = 5/12, not 2/10. To multiply, multiply the numerators and the denominators; to divide, multiply by the reciprocal.

5/6

Common denominator 6: 3/6 + 2/6 = 5/6. Adding numerators and denominators gives 2/5, which is wrong (it is smaller than 1/2).

To divide by a fraction, multiply by its reciprocal: (2/5) ÷ (4/15) = (2/5) × (15/4).

Dividing by 4/15 asks how many times 4/15 fits in the number; multiplying by 15/4 gives the same result, here 30/20 = 3/2 after simplifying.

The notation aⁿ: for an integer n ≥ 1, the product of n factors all equal to a. For a not zero, by convention a⁰ = 1 and a⁻ⁿ = 1/aⁿ.

The rules are aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ / aⁿ = aᵐ⁻ⁿ and (aᵐ)ⁿ = aᵐⁿ: exponents add for a product and multiply for a power of a power.