Law of Exponents Calculator

Exponents Law:

\[ a^m \times a^n = a^{m+n} \]

Left Side (a^m × a^n):

Right Side (a^{m+n}):

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1. What is the Law of Exponents?

The Law of Exponents states that when multiplying two exponential expressions with the same base, you can add the exponents. This is expressed as:

\[ a^m \times a^n = a^{m+n} \]

2. How Does the Calculator Work?

The calculator demonstrates the law by calculating both sides of the equation:

\[ \text{Left Side: } a^m \times a^n \] \[ \text{Right Side: } a^{m+n} \]

Where:

\( a \) — The base number
\( m \) — First exponent
\( n \) — Second exponent

Explanation: The calculator shows that both sides of the equation yield the same result, demonstrating the validity of the exponents law.

3. Importance of Exponents Law

Details: This fundamental law of exponents is crucial for simplifying exponential expressions, solving equations, and working with scientific notation in mathematics and science.

4. Using the Calculator

Tips: Enter any non-zero base and any exponents (positive, negative, or fractional). The calculator will demonstrate the law by showing both sides of the equation produce identical results.

5. Frequently Asked Questions (FAQ)

Q1: Does this law work with negative exponents?
A: Yes, the law holds true for all real number exponents, including negative and fractional exponents.

Q2: What if the base is zero?
A: The base cannot be zero when exponents are zero or negative, as this would involve division by zero.

Q3: Can this law be extended to more than two terms?
A: Yes, for example: \( a^m \times a^n \times a^p = a^{m+n+p} \)

Q4: Does this work with different bases?
A: No, the bases must be identical for this law to apply. Different bases require different approaches.

Q5: How is this law used in real-world applications?
A: This law is fundamental in scientific calculations, compound interest formulas, population growth models, and many areas of physics and engineering.