Power Rule for Exponents

What is the Power Rule for exponents?
The “power rule for exponents” refers to the rule for simplifying an expression where a power is raised to another power. It’s also sometimes called the “power of a power rule”.

The Power Rule for exponent states that when we raise a power to a power, we can multiply the exponents while keeping the base the same.

Formula:
(a^m)ⁿ = a^{m × n}
Where:
(a) is the base (any real number or variable).
(m) and (n) are the exponents (any real numbers).

How to Apply the Power Rule:

1. Identify the base and the exponents.
2. Multiply the inner exponent by the outer exponent.
3. The base remains the same.

Example:
(3²)⁵ = 3^{2 × 5} = 3¹⁰

The following diagram shows the power rule for exponents. Scroll down the page for more examples and solutions for the exponential rules.

 

Rules of Exponents
Refer to the following for more Rules of Exponents:
Rules of Exponents

• Worksheets to Practice Exponent Rules

  Printable
  Product Rule
  Quotient Rule
  Power Rule
  Negative Exponents
  Fractional exponents
  Laws of Exponents
  

  Online
  Apply Law of Exponents (multiply)
  Apply Law of Exponents (mixed)
  

Power Rule: How to raise exponents to another power.

Power of a Power - Exponent Rule

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