Class 8MathematicsChapter 12Preksha • Last-Minute Revision
Exponents and Powers
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- Same-base multiplication adds exponents.
- Same-base division subtracts exponents.
- Power of a power multiplies exponents.
- For non-zero a, a⁰ = 1.
- Negative exponent means reciprocal.
- Standard form is a × 10^n where 1 ≤ a < 10.
What You Will Learn
- Apply laws of exponents
- Interpret zero exponents
- Interpret negative exponents
- Simplify powers
- Write large and small numbers in standard form
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Exponent laws
Exponent laws shorten repeated multiplication. Always check that the bases match before adding or subtracting exponents.
Zero and negative powers
For non-zero a, a⁰ = 1. A negative exponent means reciprocal, not a negative number.
Standard form
Very large and very small numbers are easier to compare when written as a number from 1 to less than 10 multiplied by a power of 10.
Formula Sheet
Formula / Key Relations
Product law
Same base.
Quotient law
a is non-zero.
Power of a power
Multiply exponents.
Power of a product
Distribute the exponent.
Negative exponent
a is non-zero.
Standard form
Coefficient must be between 1 and 10.
Worked Examples
Standard form
Question
Write 0.00056 in standard form.
Solution
Move the decimal four places right, so exponent is -4.
Simplify
Question
Simplify (3²)⁴.
Solution
Use power of a power.
Exam Traps
Quick Revision
Quick Revision
- Same-base multiplication adds exponents.
- Same-base division subtracts exponents.
- Power of a power multiplies exponents.
- For non-zero a, a⁰ = 1.
- Negative exponent means reciprocal.
- Standard form is a × 10^n where 1 ≤ a < 10.
- Revise the formula sheet once more before attempting questions.
Compact Practice
Q1MCQModerateClass 8
2³×2⁴?
View Solution
2⁷
Q2ShortModerateClass 8
5⁶÷5²?
View Solution
5⁴
Q3ShortModerateClass 8
0.00072 in standard form?
View Solution
7.2×10^-4
Q4ApplicationModerateClass 8
(2³)⁵ = ?
View Solution
2¹⁵
Final Chapter Summary
Chapter Summary
- Same-base multiplication adds exponents.
- Same-base division subtracts exponents.
- Power of a power multiplies exponents.
- For non-zero a, a⁰ = 1.
- Negative exponent means reciprocal.
- Prioritise correct method, clean working and final units where applicable.