What Are Exponents?
An exponent is a short way of expressing repeated multiplication of the same number.
For example:
23=2×2×2=8Here, 2 is the base and 3 is the exponent (also called power or Index).
It means the number 2 is multiplied 3 times.
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Why Are Exponents Useful?
Exponents make it easy to:
- Express large numbers (like 106=1000000)
- Perform faster calculations
- Understand scientific and technical concepts
Exponents – Key Terms
| Term | Meaning |
|---|---|
| Base | The number which is multiplied (e.g., 2 in 23) |
| Exponent | The number of times the base is multiplied (e.g., 3 in 23) |
| Power | The complete expression (e.g., 23, read as “2 raised to the power 3”) |
Rules of Exponents (Laws of Exponents)
Understanding these rules makes solving exponent problems easier.
1. Multiplying Powers with Same Base
am×an=am+nExample:
23×24=23+4=27=128
2. Dividing Powers with Same Base
am/an=am-n
where a doesn't equal to 0.Example:
24/23=24-3=21=2
3. Power of a Power
(am)n=amxnExample:
(32)3=32×3=36=729
4. Power of a Product
(ab)m=am×bmExample:
(2×5)3=23×53=8×125=1000
5. Power of a Quotient
(a/b)m=am/bmExample:
(2/5)3=23/53=8/125
6. Any Number Raised to Power 0
a0=1
where a doesn't equal to 0.Example:
50=1,
1000=1
Tips to Remember
- Power means repetition of multiplication.
- Don’t confuse multiplication with addition when using exponents.
- Practice is key to mastering exponent laws.
Real-Life Applications
- Computer Science: Data storage and binary systems (e.g., 2⁸ = 256 possible values)
- Physics: Scientific notation (e.g., 6.02×1023)
- Banking & Finance: Compound interest formulas use exponents
Important Summary Points
- Convert unlike fractions before adding or subtracting.
- Always align decimal points during addition/subtraction.
- Decimal multiplication requires counting total decimal places.
- Divide decimals by removing the decimal point and adjusting accordingly.
Fun Facts – Exponents
The word “Exponent” comes from Latin exponere, meaning “to put forth”.
Activity (Exercise):
- Simplify: 34×32
2. Find: (23)2
3. Express 1000000 using exponents
5. Evaluate: (4/5)2
6. What is the value of 90?
Quiz:
Coming Soon…
Supplementary Materials:
Provide downloadable materials for learners to review:
- – PDF Guide: “Coming Soon”
- – Cheat Sheet: “Coming Soon”
- – Video Source: “JNG ACADEMY“
- – Articles: “Blog Page“
FAQs:
Q1. What is the difference between exponent and power?
They are often used interchangeably. “Exponent” refers to the number above the base, and “power” refers to the whole expression.
Q2. What is 0^0?
It is undefined in mathematics.
Q3. Can exponents be negative in Class 7?
No, negative exponents are introduced in higher classes.