Easy Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

In this easy level, we'll learn the basics of powers, exponents, and simple exponential operations.

Let's explore the powerful world of exponents!

1. Write the exponential form of 5 × 5 × 5.

5 × 5 × 5 = 5³5 × 3

Base = , Exponent =

Perfect! When a number is multiplied by itself, we write it as a power.

2. Write 7³ in expanded form.

7³ = × ×

Excellent! The exponent tells us how many times to multiply the base.

3. Simplify: 2².

2² = ×

=

Correct! 2 squared equals 4.

4. Write the base and exponent in 8⁴.

Base =

Exponent (or Power) =

Perfect! In aⁿ, 'a' is the base and 'n' is the exponent.

5. Express 81 as a power of 3.

81 = × × ×

81 = 3⁴3 × 4

Excellent! 3 × 3 × 3 × 3 = 81, so 81 = 3⁴.

6. Write 10⁵ in numeral form.

10⁵ = 10 × 10 × 10 × 10 × 10 = 100,000100000

Correct! Powers of 10 give us place values.

7. Simplify: 3¹.

3¹ = 31

Perfect! Any number raised to power 1 equals itself.

8. What is the value of any nonzero number raised to the power 0?

a⁰ = 10 (where a ≠ 0)

Excellent! Any nonzero number to the power 0 equals 1.

9. Write 1,000 as a power of 10.

1,000 = 10³10,000

Correct! 10 × 10 × 10 = 1,000.

10. Write 2 × 2 × 2 × 2 in exponential form.

2 × 2 × 2 × 2 = 2⁴2 × 4

Perfect! Count how many times 2 is multiplied.

Drag each power to its correct value:

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Simplify: (a² × a³).

Law: aᵐ × aⁿ = aᵐ⁺ⁿaᵐⁿ

a² × a³ = a²⁺³²×³

= a⁵⁶

Perfect! Add the exponents when multiplying with the same base.

2. Simplify: (x⁴ ÷ x²).

Law: aᵐ ÷ aⁿ = aᵐ⁻ⁿaᵐ⁺ⁿ

x⁴ ÷ x² = x⁴⁻²⁴⁺²

= x²⁶

Excellent! Subtract the exponents when dividing with the same base.

3. Simplify: (2³ × 3²).

Step 1: Calculate 2³ =

Step 2: Calculate 3² =

Step 3: Multiply: 8 × 9 =

Great! When bases are different, calculate each power first.

4. Simplify: (5²)³.

Law: (aᵐ)ⁿ = aᵐⁿaᵐ⁺ⁿ

(5²)³ = 5²×³²⁺³

= 5⁶⁵

Perfect! Multiply the exponents when raising a power to a power.

5. Simplify: 10³ ÷ 10².

10³ ÷ 10² = 10³⁻²³⁺²

= 10¹⁵

=

Excellent! Subtract exponents when dividing.

6. Simplify: (3² × 3³) ÷ 3².

Step 1: Multiply first: 3² × 3³ = 3⁵⁶

Step 2: Divide: 3⁵ ÷ 3² = 3³⁷

=

Great! Apply operations step by step.

7. Simplify: (2⁵ ÷ 2³).

2⁵ ÷ 2³ = 2⁵⁻³⁵⁺³

= 2²⁸

=

Perfect! 2² = 4.

8. Write the laws of exponents for multiplication and division.

Multiplication: aᵐ × aⁿ =

Division: aᵐ ÷ aⁿ =

Excellent! These are the fundamental laws of exponents.

9. Find the value of (4²) × (4³).

4² × 4³ = 4⁵⁶

4⁵ = 10241000

Great! 4⁵ = 4 × 4 × 4 × 4 × 4 = 1024.

10. Simplify: (x³)².

(x³)² = x³×²³⁺²

= x⁶⁵

Perfect! Multiply the exponents.

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. (a³ × a²) =

(a) a⁵ (b) a⁶ (c) a³ (d) a⁴

Correct! When multiplying, add the exponents: 3 + 2 = 5.

7. (x⁵ ÷ x³) =

(a) x⁸ (b) x² (c) x⁵ (d) x³

Perfect! When dividing, subtract the exponents: 5 – 3 = 2.

8. The value of 6¹ =

(a) 0 (b) 1 (c) 6 (d) 36

Correct! Any number to the power 1 equals itself.

9. The base of 2⁴ is:

(a) 2 (b) 4 (c) 8 (d) None

Excellent! In aⁿ, 'a' is always the base.

10. 2⁰ × 3⁰ =

(a) 0 (b) 1 (c) 2 (d) 3

Perfect! 2⁰ = 1 and 3⁰ = 1, so 1 × 1 = 1.

🎉 Fantastic Work! You've Mastered Basic Powers and Exponents!

Here's what you learned:

• Exponential Notation:

  Definition:

  • aⁿ means 'a' multiplied by itself 'n' times
  • Example: 5³ = 5 × 5 × 5 = 125

  Parts:

  • Base (a): The number being multiplied
  • Exponent (n): How many times to multiply
  • In 2⁴: Base = 2, Exponent = 4

• Basic Exponent Rules:

  Multiplication Rule:

  • aᵐ × aⁿ = aᵐ⁺ⁿ
  • Example: 3² × 3³ = 3⁵
  • Add exponents when bases are the same

  Division Rule:

  • aᵐ ÷ aⁿ = aᵐ⁻ⁿ
  • Example: 5⁴ ÷ 5² = 5²
  • Subtract exponents when bases are the same

  Power of a Power Rule:

  • (aᵐ)ⁿ = aᵐⁿ
  • Example: (2³)² = 2⁶
  • Multiply exponents

• Special Cases:

  Power of 1:

  • a¹ = a
  • Example: 7¹ = 7
  • Any number to power 1 equals itself

  Power of 0:

  • a⁰ = 1 (where a ≠ 0)
  • Example: 5⁰ = 1, 100⁰ = 1
  • Any nonzero number to power 0 equals 1

• Powers of 10:

  • 10¹ = 10
  • 10² = 100
  • 10³ = 1,000
  • 10⁴ = 10,000
  • Powers of 10 help with place values

• Common Powers to Remember:

  • 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32
  • 3² = 9, 3³ = 27, 3⁴ = 81
  • 4² = 16, 4³ = 64
  • 5² = 25, 5³ = 125

• Calculating with Exponents:

  • When bases are same: Use exponent rules
  • When bases are different: Calculate each power separately
  • Example: 2³ × 3² = 8 × 9 = 72

• Common Mistakes to Avoid:

  • Don't confuse 2³ with 2 × 3 = 6 (2³ = 8)
  • Don't add exponents when multiplying different bases
  • Remember: a⁰ = 1, not 0
  • Don't forget to apply the rule correctly: add for multiplication, subtract for division

Understanding exponents is crucial for advanced mathematics, science, and technology!