Exponent Examples for Beginners (20 Solved Questions)

The fastest way to learn exponents is to see many small examples and try a few yourself. This page collects exponent examples for beginners, arranged from very easy to a little harder, with every step shown. The examples use Indian settings such as rupees, lakh and crore, school plots, phone storage and bank deposits, so the numbers feel familiar.

Before you begin, remember the one idea behind all of them: aⁿ means a multiplied by itself n times. If you want a quick check on any answer, use the free exponent calculator on DigiToolkit.

Level 1: Squares and Cubes

Start with the two most common powers. Squares come from multiplying a number by itself once, and cubes from multiplying it twice.

Number	Square	Cube
2	4	8
3	9	27
4	16	64
5	25	125
6	36	216
7	49	343
8	64	512
9	81	729
10	100	1,000

Example 1. A square plot in Nagpur has each side of 40 feet. Its area is 40² = 1,600 square feet.

Example 2. A cubical water tank has each edge of 3 metres. Its volume is 3³ = 27 cubic metres, which equals 27,000 litres.

Key takeaway: Learn the square and cube table above by heart. Almost every beginner exponent question uses these numbers.

Level 2: Higher Powers of Small Numbers

Example 3: 2⁸. Double step by step: 2, 4, 8, 16, 32, 64, 128, 256. So 2⁸ = 256. This is the number of values one byte of computer memory can hold.

Example 4: 3⁵. Triple step by step: 3, 9, 27, 81, 243. So 3⁵ = 243.

Example 5: 5⁴. 5 x 5 = 25, 25 x 5 = 125, 125 x 5 = 625. So 5⁴ = 625.

Notice the pattern: write the running total after each multiplication. It is a simple way to avoid slips with longer powers.

Level 3: Powers of Ten, Lakh and Crore

Powers of ten are the easiest of all, because the exponent equals the number of zeros.

• 10² = 100 (one hundred)
• 10³ = 1,000 (one thousand)
• 10⁵ = 1,00,000 (one lakh)
• 10⁷ = 1,00,00,000 (one crore)
• 10⁹ = 100 crore (one arab)
• 10¹² = one lakh crore

Example 6. A village receives a grant of Rs. 25 lakh. Write it as 25 x 10⁵ = 25,00,000 rupees.

Example 7. A company reports turnover of 8 x 10⁸ rupees. That is 8 followed by eight zeros, or 80 crore rupees.

Level 4: Zero, One and Negative Exponents

Example 8: 17⁰. Any non-zero number to the power 0 is 1. So 17⁰ = 1.

Example 9: 9¹. A power of 1 leaves the number as it is. So 9¹ = 9.

Example 10: 4^-2. Flip it into a fraction: 1 / 4² = 1/16 = 0.0625.

Example 11: 10^-3. This equals 1/1000 = 0.001. In science, one millimetre is 10^-3 metres.

Level 5: Using the Laws

Example 12: 3² x 3⁴. The bases match, so add the exponents: 3⁶ = 729.

Example 13: 7⁹ / 7⁶. The bases match, so subtract: 7³ = 343.

Example 14: (2³)². A power of a power, so multiply the exponents: 2⁶ = 64.

Example 15: (2 x 3)². Apply the power to each factor: 2² x 3² = 4 x 9 = 36, which matches 6².

For the full list of rules and why they work, see our guide on the exponent formula and laws.

Level 6: Real-Life Money Examples

Example 16: Fixed deposit. Sunita invests Rs. 2,00,000 for 4 years at 7.5% a year, compounded yearly. The factor is 1.075⁴. Work it out: 1.075 x 1.075 = 1.155625; 1.155625 x 1.155625 = 1.33547. The maturity amount is 2,00,000 x 1.33547 = Rs. 2,67,094 (rounded). The interest earned is about Rs. 67,094.

Example 17: Falling value. A new scooter costs Rs. 90,000 and loses 10% of its value every year. After 3 years its value is 90,000 x 0.9³ = 90,000 x 0.729 = Rs. 65,610. Here the base is below 1, so the number shrinks. This is how depreciation works.

Example 18: Inflation. If prices rise 6% a year, something that costs Rs. 100 today costs about 100 x 1.06¹⁰ = Rs. 179 in ten years. The Reserve Bank of India aims to keep inflation near 4%, and even a small yearly rate adds up through the exponent.

Level 7: Computer Memory and Data

Example 19. A pen drive of 32 GB holds 32 x 2¹⁰ MB = 32 x 1,024 = 32,768 MB in binary terms.

Example 20. A password of 6 digits can take 10⁶ = 10,00,000 different values, which is why short PINs are weaker than longer ones. A 4 digit PIN has only 10⁴ = 10,000 possibilities.

Level 8: Decimals, Fractions and Scientific Notation

Once the basics feel easy, try bases that are not whole numbers. The same rule applies: multiply the base by itself as many times as the exponent says.

Example 21: 0.5³. 0.5 x 0.5 = 0.25, and 0.25 x 0.5 = 0.125. So 0.5³ = 0.125. A base below 1 gives a smaller answer each time you raise the power, which is why decay and depreciation use bases like 0.9.

Example 22: (1/2)⁴. Raise both the top and bottom: 1⁴ / 2⁴ = 1/16. If a bucket of water is halved four times, one sixteenth remains.

Example 23: 1.1². 1.1 x 1.1 = 1.21. Raising by 10% twice gives a 21% total rise, not 20%. This is the small extra that compounding adds, and it is the reason two successive price hikes of 10% cost more than one hike of 20%.

Example 24: Writing 0.00045 in scientific notation. Move the decimal four places right to get 4.5, so the number is 4.5 x 10^-4. The negative power shows the number is small.

Example 25: Writing 6,02,00,000 in scientific notation. Move the decimal seven places left to get 6.02, so the number is 6.02 x 10⁷, which is about 6 crore.

Example 26: Comparing two numbers. Which is larger, 3⁴ or 4³? Work them out: 3⁴ = 81 and 4³ = 64. So 3⁴ is larger, even though the base 4 looks bigger. Do not guess; compute and compare.

How to Read Your Own Answers

After each example, ask three short questions. First, does the size make sense? A base above 1 with a positive power should give a bigger number, and a base between 0 and 1 should give a smaller one. Second, is the sign right? A negative base with an odd power gives a negative result, and with an even power a positive one. Third, did I use the correct law? If the bases differ, the product and quotient laws do not apply directly. Asking these three questions takes five seconds and catches most beginner errors before they reach your answer sheet.

Practice Questions with Answers

Try these on your own, then check the answers below.

1. Find 8³.
2. Find 2¹⁰.
3. Write 3,50,000 using a power of ten.
4. Simplify 5⁷ / 5⁵.
5. Find 2^-4.
6. What is (-3)³?

Answers: (1) 512. (2) 1,024. (3) 3.5 x 10⁵. (4) 5² = 25. (5) 1/16 = 0.0625. (6) -27.

Benefits of Practising with Examples

Worked examples build pattern recognition. After a dozen questions, you begin to see that most problems fall into a handful of types: plain powers, powers of ten, negative powers, law-based simplification and growth. This makes exam questions feel familiar. Examples also reveal your weak spots early, so you can fix them before a board exam or a job test. Finally, real-life cases such as deposits and depreciation show why the topic is worth your time.

Challenges and Limitations

Examples alone cannot cover every variation. A student who copies steps without grasping the reason may struggle when the question is worded differently. Large powers are also tedious by hand, so beginners may lose heart. The remedy is to move from small cases to bigger ones slowly, and to use a calculator for the final check.

Common Mistakes to Avoid

1. Multiplying base and exponent. 5³ is 125, not 15.
2. Ignoring brackets. (-3)² = 9 but -3² = -9.
3. Adding unlike bases. 2³ x 3³ is not 5⁶. It is 8 x 27 = 216.
4. Forgetting that zero power is 1. It is not zero.
5. Using 6% as 6. In growth questions, use 1.06, not 6.
6. Skipping the sense check. If a 7% deposit gives a 300% gain in 3 years, something is wrong.

Best Practices and Expert Recommendations

1. Practise daily for ten minutes. Short, regular sessions beat one long cram night.
2. Write every multiplication step. Running totals prevent slips.
3. Memorise powers of 2 and 10. They appear everywhere in exams and computing.
4. Move from easy to hard. Do not jump to law-based questions before squares and cubes feel natural.
5. Check with a tool. Confirm results using the calculator, then read what is an exponent if any idea is still hazy.
6. Make your own questions. Create problems about your own savings or screen sizes to deepen understanding.

Conclusion

These twenty examples cover nearly every kind of beginner exponent question: squares, cubes, powers of ten, zero and negative powers, law-based simplification, and real money and data cases. Work through them in order, try the practice set, and use a calculator only to confirm your answers. With steady practice, exponents will quickly become one of the easier parts of maths.

FAQs

What are some easy examples of exponents?
Easy examples include 2³ = 8, 3² = 9, 5² = 25 and 10³ = 1,000. Each one is just repeated multiplication of the base. Squares and cubes are the best place to start.

How do I solve exponent problems for beginners?
Write the base as many times as the exponent says and multiply step by step, noting the running total. For laws-based questions, check whether the bases match and then add, subtract or multiply exponents. A quick calculator check helps confirm the answer.

What is 2 to the power 10?
2 to the power 10 is 1,024. It is the number of bytes in a kilobyte in the binary system. It is also a common exam and computing number.

How do I write 5 crore using exponents?
Five crore is 5 x 10⁷, which equals 5,00,00,000. A crore is 10⁷, so you simply multiply 5 by that power of ten.

What is a real life example of an exponent?
Compound interest on a fixed deposit is a common example. Rs. 1,00,000 at 8% for 5 years becomes 1,00,000 x 1.08⁵, about Rs. 1,46,933. Depreciation and inflation use the same idea.

How can I practise exponents at home?
Use the practice questions here, then make your own using prices, plot sizes and storage. Check each answer with a free online calculator. Ten minutes a day is enough to build real confidence.