1. What is the Power of a Power Rule?

The Power of a Power Rule is a fundamental exponent rule in algebra that states when you raise a power to another power, you multiply the exponents. The general form is \((a^m)^n = a^{m \times n}\).

2. How Does the Calculator Work?

The calculator applies the power of a power rule:

Where:

• \( a \) — The base number
• \( m \) — The first exponent
• \( n \) — The second exponent

Explanation: The rule simplifies expressions where an exponential expression is raised to another power by multiplying the exponents.

3. Importance of the Rule

Details: This rule is essential for simplifying complex exponential expressions, solving equations with exponents, and working with scientific notation. It's a foundational concept in algebra and higher mathematics.

4. Using the Calculator

Tips: Enter the base number and both exponents. The calculator will compute the result of raising the base to the first exponent, then raising that result to the second exponent (which is equivalent to raising the base to the product of the exponents).

5. Frequently Asked Questions (FAQ)

Q1: Does this rule work with negative exponents?
A: Yes, the power of a power rule applies to all real number exponents, including negative and fractional exponents.

Q2: What if the base is negative?
A: The rule still applies, but be cautious with even exponents which will make the result positive.

Q3: Can this rule be used with variables?
A: Yes, the rule works the same way with variables as it does with numbers.

Q4: How is this different from the product of powers rule?
A: The product of powers rule (\(a^m \times a^n = a^{m+n}\)) deals with multiplying terms with the same base, while the power of a power rule deals with exponents of exponents.

Q5: Does this rule apply to more than two exponents?
A: Yes, for example \((a^m)^n)^p = a^{m \times n \times p}\).