Exponents and Powers 8 Maths — Revision Notes
Exponents and powers provide a compact way to express repeated multiplication. They are fundamental to algebra, science, and technology.
TL;DR: Exponents and powers provide a compact way to express repeated multiplication. They are fundamental to algebra, science, and technology.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Exponents and powers provide a compact way to express repeated multiplication. They are fundamental to algebra, science, and technology.
Basic Concepts
- Exponent or power is the number of times a base is multiplied by itself
- In 2 to the power 5, 2 is the base and 5 is the exponent
- 2 to the power 5 equals 2 times 2 times 2 times 2 times 2 equals 32
- Any non-zero number to the power 0 equals 1
- Any number to the power 1 equals that number
Laws of Exponents
- Product rule: a to power m times a to power n equals a to power m plus n
- Quotient rule: a to power m divided by a to power n equals a to power m minus n
- Power rule: (a to power m) to power n equals a to power m times n
- Product to a power: (ab) to power m equals a to power m times b to power m
- Quotient to a power: (a/b) to power m equals a to power m divided by b to power m
Negative and Fractional Exponents
- Negative exponent: a to power negative n equals 1 divided by a to power n
- 2 to power negative 3 equals 1/8
- Fractional exponent: a to power 1/n is the nth root of a
- a to power m/n equals nth root of a to power m
- 2 to power 1/2 equals square root of 2 approximately 1.414
Scientific Notation
- Scientific notation expresses large and small numbers in compact form
- Form: a times 10 to power n where 1 is less than or equal to a and a is less than 10
- 500000 in scientific notation is 5 times 10 to power 5
- 0.0007 in scientific notation is 7 times 10 to power negative 4
- Used extensively in science, physics, and astronomy for very large or small quantities
Applications of Exponents
- Compound interest calculations use exponential growth formulas
- Population growth modeled using exponential functions
- Radioactive decay described using negative exponentials
- Computer science uses powers of 2 for binary and data storage units
- Technology follows Moore's Law, which is exponential progression
Key Terms
- Exponent: Number indicating how many times the base is multiplied by itself
- Base: Number that is repeatedly multiplied in exponential notation
- Power: Result of raising a base to an exponent
- Scientific Notation: Way of expressing numbers as product of a decimal and power of 10
Frequently Asked Questions
Why does any number to the power 0 equal 1?
Using the quotient rule: a to power n divided by a to power n equals a to power 0. Since a to power n divided by itself equals 1, a to power 0 equals 1.
What does a negative exponent mean?
A negative exponent means the reciprocal of the base raised to the positive exponent. For example, 2 to power negative 3 equals 1/(2 to power 3) which equals 1/8.
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