What are the topics covered in the curriculum related to exponents and number operations?

Steps to Solve

1. Identify the Relevant Concepts

From the question, we need to recognize the key mathematical concepts: prime factorization, HCF (Highest Common Factor), LCM (Lowest Common Multiple), and operations with factors.

2. Prime Factorization

To find prime factors, break down any number into a product of prime numbers. For example, for the number 28:

• $28 = 2 \times 14$
• $14 = 2 \times 7$ Therefore, the prime factorization of 28 is $2^2 \times 7$.

3. Finding HCF

To find the HCF of two or more numbers, list their prime factors and multiply the lowest powers of all prime factors common to both numbers.

• For example, if finding the HCF of 24 ($2^3 \times 3^1$) and 36 ($2^2 \times 3^2$):
• Common prime factors: $2^2$ and $3^1$
• HCF = $2^2 \times 3^1 = 4 \times 3 = 12$.

4. Finding LCM

To find the LCM, list all prime factors, taking the highest powers of each prime factor.

• Using the previous example (24 and 36):
• LCM = $2^3 \times 3^2 = 8 \times 9 = 72$.

5. Understanding Exponents

Exponents indicate how many times a number (the base) is multiplied by itself. For example, $a^n$ means $a$ multiplied by itself $n$ times.

6. Order of Operations

When solving equations, follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).