Interactive Exponents and Powers Worksheet

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

Exponents and powers are a shorthand way of writing repeated multiplication. Understanding their laws helps us solve complex mathematical expressions efficiently.

First, let's practice basic exponent notation and simple calculations.

1. Express 625 in exponential form with base 5. 5453

Awesome! 54 = 625 is correct.

2. Find the value of: 23 × 24 27212

Great job! 23 × 24 = 27 = 128.

3. Simplify and write in exponential form: 7⁵ ÷ 7² 73710

Perfect! 75 ÷ 72 = 73 = 343.

4. Write the value of 10−2.

Excellent! 10−2 = 1102 = 0.01.

5. Evaluate: −32

Super! −32 = 9 is correct.

6. Express 116 as a power of 2. 2−424

That's correct! 116 = 2−4.

7. What is the value of (50 + 30)?

Well done! Any number to power 0 equals 1, so 1 + 1 = 2.

8. Express 243 as a power of 3. 35343−5

Brilliant! 35 = 243 is the solution.

9. Write the standard form of 2.5 × 10⁶.

You nailed it! 2.5 × 106 = 2,500,000.

10. Write the multiplicative inverse of 3−2. 3213−2

Perfect! The multiplicative inverse of 3−2 is 32 = 9.

Drag each expression to its corresponding exponent law:

Part B: Short Answer Questions (2 Marks Each)

1. Simplify: (23 × 2−5) ÷ 2−2

First, we need to combineaddsubtract the exponents using laws.

Using product law: 23 × 2−5 = 2−22−15

Now dividing: 2⁻² ÷ 2⁻² =

Excellent! The answer is 1.

2. Simplify and express in exponential form: 323

Using power law: 323 = 3635

Converting to numerical form: 36 =

Great work! (3²)³ = 3⁶ = 729.

3. Express 1250000 in standard form.

Standard form = 1.25 × 10612.5 × 106

4. Simplify and express in positive exponent form: (5−1 × 25) ÷ (52)

First, express 25 as of 5.

Where 25 = 5253

So we have: (5−1 × 52) ÷ 52 = 15151

Therefore the answer is:

Great! The answer in positive exponent form is 15.

Part C: Long Answer Questions (4 Marks Each)

1. Simplify and express with positive exponents: (3−2 × 9) ÷ (33) ÷ 3−1

First, express 9 as of 3.

Where 9 = 3233

Simplifying (3−2 × 32) ÷ (33) ÷ 3−1 = 13232

In positive exponent form =

Excellent! The simplified form is 1/9.

2. Convert the following into standard form:

(a) 0.0000071 = 7.1 × 10−67.1 × 106

(b) 5250000000 = 5.25 × 1095.25 × 108

Perfect! Both conversions are correct.

3. Simplify using laws of exponents: [(25 × 34) ÷ 62] ÷ (2 × 3)

Final Answer is:

Fantastic! The simplified answer is 12.

4. A computer can process 46 instructions per second. How many instructions can it process in 10 seconds?

instructions per second: 46 =

In 10 seconds: instructions

Awesome! The computer processes 40,960 instructions in 10 seconds.

Test your understanding with these multiple choice questions:

For each question, click on the correct answer:

1. Simplify: (4−1 × 42) ÷ 4

(a). 1 (b). 4 (c). 0 (d). 2

Excellent! (4−1 × 42) ÷ 4 = 41 ÷ 4 = 40 = 1.

2. Which of the following is correct?

(a)a0 = 1 (b) a0 = 0 (c) a0 = a (d) a0 = –1

Excellent! Any non-zero number raised to power 0 equals 1.

3. The expression (3³)² equals:

(a) 35 (b) 36 (c) 93 (d) 63

Perfect! Using power law: 332 = 33·2 = 36.

4. 8. What is the value of (103 × 10−2)

(a). 10 (b). 100 (c). 1000 (d). 1

Great! Using product law: 103 × 10−2 = 101 = 10.

5. Which of these is the expanded form of 7 × 106?

(a). 700000 (b). 7000000 (c). 70000 (d). 70000000

Fantastic! 7 × 106 = 7 × 1,000,000 = 7,000,000.