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Laws of Indices

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Laws of Indices

Laws of Indices

Mathematical indices and exponents illustration

📚 Part 1: Understanding the Laws of Indices

1. Complete the following rules by filling in the blanks:

Product Rule: am × an = a_______

Power Rule: (am)n = a_______

Zero Index Rule: a0 = _______ (where a ≠ 0)

2. Circle the correct answer for each expression:

a) 32 × 34 =

36

38

96

66

b) (23)2 =

25

26

46

82

c) 70 =

0

1

7

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🔢 Part 2: Applying the Product Rule

3. Simplify the following expressions using the product rule. Show your working:

a) x3 × x5 =

b) 24 × 23 =

c) a7 × a2 × a1 =

d) m6 × m0 =

⚡ Part 3: Applying the Power Rule

4. Simplify the following expressions using the power rule. Show your working:

a) (x4)3 =

b) (52)4 =

c) (y3)0 =

d) (a1)8 =

🎯 Part 4: Zero Index Rule Practice

5. Evaluate the following expressions:

a) 150 = _______

b) (-8)0 = _______

c) (3x)0 = _______ (where x ≠ 0)

d) 4 × 90 = _______

6. Explain in your own words why any non-zero number raised to the power of zero equals 1:

🧩 Part 5: Mixed Practice

7. Simplify the following expressions. Show all working:

a) 32 × 30 × 34 =

b) (x5)2 × x3 =

c) (23)0 × 25 =

d) a4 × (a2)3 =

8. Check all expressions that equal 1:

1000

15

01

(-25)0

(xy)0 where x,y ≠ 0

🚀 Part 6: Challenge Problems

9. Match each expression on the left with its simplified form on the right:
1. x3 × x2 × x0
2. (y4)2
3. 50 + 30
4. (a0)10
A. y8
B. 2
C. x5
D. 1
10. Real-world application: In computer science, data storage is often measured in powers of 2. If a computer has 23 gigabytes of RAM and you want to calculate (23)2 gigabytes, how much storage would that represent? Show your calculation:

Answer: _______ gigabytes

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