BECE Mathematics 2022 Paper

Prime number is a number that is divisible only by itself and $1$ (e.g. $2,3,5,7,11$ )To express a number as a product of prime factors express the number as a multiple of prime numbers and simplify in a form of indexes$108\;=2 \times 54$$108\;=2 \times 2 \times 27$$108\;=2 \times 2 \times 3 \times 9$$108\;=2 \times 2 \times 3 \times 3 \times 3$Now apply the law of indexes$a^m \times a^n=a^{m+n}$Thus if the bases are the same and are multiplying, you can add the powers$a=a^1$Thus every number is raised to the power 1$\;108=2 \times 2 \times 3 \times 3 \times 3=2^1 \times 2^1 \times 3^1 \times 3^1 \times 3^1$$\;108=2^{1+1} \times 3^{1+1+1}$$\;108=2^2 \times 3^3$