Introduction to the Laws of Exponents
The laws of exopnents explain how numbers with powers behave. Students often ask, what are the laws of exponents in math? These rules make solving problems easier. Mathematics Study Material for Hearing Impaired Students covers these laws with simple explanations. Moreover, mathematics for hearing impaired students uses visual aids to ensure clear understanding. Therefore, it becomes easier to practice with the best study material for hearing impaired students.
Application of the Laws of Exponents
The laws of exopnents are used in algebra, geometry, and daily calculations. For example, they help simplify multiplication and division of powers. Mathematics Study Material for Hearing Impaired Students includes step-by-step examples. Additionally, mathematics for hearing impaired students provides guided activities for clarity. With practice, the best study material for hearing impaired students allows learners to master each law effectively.
📚 Laws of Exponents for Real Numbers
Master the fundamental rules that govern exponential expressions!
🎯 What Are Exponents?
An exponent tells us how many times to multiply a number by itself. In the expression an, ‘a’ is called the base and ‘n’ is called the exponent or power.
Visual Representation:
Base = 5, Exponent = 3, Result = 125
The Laws of Exponents are mathematical rules that help us simplify and manipulate expressions involving powers. These laws are essential for algebra, calculus, and many real-world applications including scientific notation, compound interest calculations, and exponential growth models.
Understanding these laws allows us to:
- Simplify complex exponential expressions
- Solve exponential equations efficiently
- Work with scientific notation
- Understand growth and decay patterns in nature and finance
- Prepare for advanced mathematics topics
📜 The Seven Laws of Exponents
When multiplying powers with the same base, add the exponents.
Example: 32 × 34 = 32+4 = 36 = 729
When dividing powers with the same base, subtract the exponents.
Example: 75 ÷ 72 = 75-2 = 73 = 343
When raising a power to another power, multiply the exponents.
Example: (23)4 = 23×4 = 212 = 4096
When raising a product to a power, raise each factor to that power.
Example: (3 × 4)2 = 32 × 42 = 9 × 16 = 144
When raising a quotient to a power, raise both numerator and denominator to that power.
Example: (6/2)3 = 63 / 23 = 216 / 8 = 27
Any non-zero number raised to the power of zero equals 1.
Example: 1000 = 1, (-5)0 = 1
A negative exponent means “take the reciprocal and make the exponent positive.”
Example: 2-3 = 1/23 = 1/8 = 0.125
✅ Solved Examples
Simplify: 53 × 57
Step 1: Identify the rule – Product Rule (same base)
Step 2: Apply the rule: am × an = am+n
Step 3: Add exponents: 53 × 57 = 53+7 = 510
Answer: 510 = 9,765,625
Simplify: (34)2
Step 1: Identify the rule – Power of a Power Rule
Step 2: Apply the rule: (am)n = am×n
Step 3: Multiply exponents: (34)2 = 34×2 = 38
Answer: 38 = 6,561
Simplify: 86 ÷ 82
Step 1: Identify the rule – Quotient Rule (same base)
Step 2: Apply the rule: am ÷ an = am-n
Step 3: Subtract exponents: 86 ÷ 82 = 86-2 = 84
Answer: 84 = 4,096
Simplify: (2 × 6)3
Step 1: Identify the rule – Power of a Product Rule
Step 2: Apply the rule: (ab)n = an × bn
Step 3: Distribute the exponent: (2 × 6)3 = 23 × 63
Step 4: Calculate: 23 × 63 = 8 × 216 = 1,728
Answer: 1,728
Simplify: 4-2
Step 1: Identify the rule – Negative Exponent Rule
Step 2: Apply the rule: a-n = 1/an
Step 3: Convert: 4-2 = 1/42
Step 4: Calculate: 1/42 = 1/16 = 0.0625
Answer: 1/16 or 0.0625
🎯 Practice Problems
Click “Show Answer” to reveal the solution for each problem:
🎓 Quick Memory Tips
ADD the exponents
SUBTRACT the exponents
MULTIPLY the exponents
Always equals 1