BECE Mathematics 2022 Paper

Concept:To express a number as a product of prime factors, divide it repeatedly by the smallest prime numbers until only 1 remains.Explanation:Start with $108$ and divide by the smallest prime, which is $2$.$108 = 2 \times 54$$54$ is still even, so divide by $2$ again.$108 = 2 \times 2 \times 27$Now $27$ is not divisible by $2$, so divide by the next prime, $3$.$27 = 3 \times 9$ and $9 = 3 \times 3$Therefore:$108 = 2 \times 2 \times 3 \times 3 \times 3$Write each repeated factor using exponents.$2 \times 2 = 2^2$ and $3 \times 3 \times 3 = 3^3$So, $108 = 2^2 \times 3^3$This uses the law of indices: $a^m \times a^n = a^{m+n}$.Answer:$108 = 2^2 \times 3^3$Therefore, the correct option is A.