Power Of Exponents Calculator

Power Of Exponents Formula:

\[ Result = (a^b)^c = a^{b \times c} \]

Result:

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1. What is the Power Of Exponents Rule?

The power of exponents rule states that when raising a power to another power, you multiply the exponents. This is expressed mathematically as \((a^b)^c = a^{b \times c}\). This fundamental rule of exponents simplifies complex exponential expressions.

2. How Does the Calculator Work?

The calculator uses the power of exponents formula:

\[ Result = (a^b)^c = a^{b \times c} \]

Where:

\( a \) — Base number
\( b \) — First exponent
\( c \) — Second exponent

Explanation: The calculator first multiplies the two exponents (b × c), then raises the base (a) to the product of these exponents.

3. Importance of Exponents Calculation

Details: Understanding and applying exponent rules is crucial in algebra, scientific notation, compound interest calculations, exponential growth/decay problems, and many areas of mathematics and science.

4. Using the Calculator

Tips: Enter the base value and both exponents. The base cannot be zero when dealing with negative exponents. All values can be positive or negative numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the base is negative?
A: The calculator handles negative bases correctly. For example, (-2)^3 = -8, and ((-2)^3)^2 = (-8)^2 = 64.

Q2: Can I use fractional exponents?
A: Yes, the calculator supports fractional exponents. For example, (4^0.5)^2 = (2)^2 = 4.

Q3: What is the result when the exponent is zero?
A: Any non-zero number raised to the power of zero equals 1. For example, (5^2)^0 = 25^0 = 1.

Q4: How does the calculator handle very large numbers?
A: The calculator uses PHP's pow() function which can handle large numbers within the limits of floating-point arithmetic.

Q5: Can this rule be applied to more than two exponents?
A: Yes, the rule extends to any number of exponents: (a^b)^c)^d = a^{b×c×d}, and so on.