Exponents Calculator
Simplify and evaluate expressions with multiple exponents using exponent rules
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Expression:
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Exponent Rules Reference
| Rule Name | Formula | Description |
|---|---|---|
Powers of 2
Powers of 10
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About Exponents Calculator
What is an Exponents Calculator?
An exponents calculator is a comprehensive mathematical tool for working with expressions involving multiple exponents. Unlike a basic power calculator, this tool helps you simplify complex exponential expressions, apply exponent rules systematically, and evaluate compound expressions.
How to Use This Calculator
- Select the operation mode: Choose from simplification, multiplication, division, or power of power
- Enter your values: Input bases and exponents as required by the selected mode
- View instant results: Get simplified expressions with step-by-step explanations
- Learn the rules: Understand which exponent rules are applied
Key Exponent Rules This Calculator Uses
1. Product Rule (Multiplication)
When multiplying expressions with the same base, add the exponents:
- aᵐ × aⁿ = aᵐ⁺ⁿ
- Example: 2³ × 2⁴ = 2³⁺⁴ = 2⁷ = 128
2. Quotient Rule (Division)
When dividing expressions with the same base, subtract the exponents:
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- Example: 5⁶ ÷ 5² = 5⁶⁻² = 5⁴ = 625
3. Power of a Power Rule
When raising a power to another power, multiply the exponents:
- (aᵐ)ⁿ = aᵐˣⁿ
- Example: (3²)⁴ = 3²ˣ⁴ = 3⁸ = 6561
4. Power of a Product Rule
When raising a product to a power, distribute the exponent:
- (ab)ⁿ = aⁿ × bⁿ
- Example: (2×3)⁴ = 2⁴ × 3⁴ = 16 × 81 = 1296
5. Power of a Quotient Rule
When raising a quotient to a power, apply the exponent to both:
- (a/b)ⁿ = aⁿ/bⁿ
- Example: (4/2)³ = 4³/2³ = 64/8 = 8
6. Negative Exponent Rule
A negative exponent means take the reciprocal:
- a⁻ⁿ = 1/aⁿ
- Example: 2⁻³ = 1/2³ = 1/8
7. Zero Exponent Rule
Any non-zero number to the zero power equals 1:
- a⁰ = 1 (where a ≠ 0)
- Example: 999⁰ = 1
Common Applications
- Scientific notation: Working with very large or small numbers
- Algebraic simplification: Simplifying polynomial and exponential expressions
- Computer science: Understanding algorithm complexity (Big O notation)
- Physics and engineering: Calculating compound effects and growth rates
- Finance: Computing compound interest and growth
Frequently Asked Questions
What's the difference between Exponent Calculator and Exponents Calculator?
The basic Exponent Calculator computes a single base^power calculation. This Exponents Calculator helps you work with multiple exponents, simplify expressions, and apply exponent rules to compound expressions.
Can I simplify expressions with different bases?
Exponent rules for combining terms only apply to expressions with the same base. For different bases, you must evaluate each expression separately.
How do I handle expressions with multiple operations?
Follow the order of operations (PEMDAS): Parentheses, Exponents (including powers of powers), Multiplication and Division (left to right), Addition and Subtraction.
Tip: Use this calculator to verify your algebraic simplifications and understand which exponent rules apply to different types of expressions.