Exponents (Powers)
Repeated multiplication of the same base.
Key idea
Repeated multiplication of the same base.
In depth
An exponent counts how many copies of the base are multiplied together: aⁿ = a × a × ... × a. It is a shorthand for repeated multiplication, just as multiplication abbreviates repeated addition.
Worked example
2⁵ = 2×2×2×2×2 = 32.
Formula
Real-world uses
- Describing compound growth, computer memory sizes such as 2^10 bytes and very large or small measurements
Common mistake
Writing 2⁵ = 2×5 = 10. The exponent counts multiplications, not a factor.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Exponents (Powers)?
Repeated multiplication of the same base. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Exponents (Powers)?
The key formula is aⁿ = a × a × … × a (n times).
Where is Exponents (Powers) used in real life?
Real-world examples: Describing compound growth, computer memory sizes such as 2^10 bytes and very large or small measurements.
What should I learn before Exponents (Powers)?
Make sure you are comfortable with Euclidean Algorithm, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Exponents (Powers)?
Writing 2⁵ = 2×5 = 10. The exponent counts multiplications, not a factor.
How can I practise Exponents (Powers)?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Exponents (Powers)?
Move on to Square Numbers and Roots next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.