1 Answer
The rule "power of a power" in mathematics states that when you raise a power to another power, you multiply the exponents. The rule can be written as:
\[
(a^m)^n = a^{m \times n}
\]
Where:
Example:
\[
(2^3)^2 = 2^{3 \times 2} = 2^6 = 64
\]
In this example:
So, the "power of a power" rule helps simplify expressions like this by multiplying the exponents.
\[
(a^m)^n = a^{m \times n}
\]
Where:
- \( a \) is the base,
- \( m \) is the first exponent,
- \( n \) is the second exponent.
Example:
\[
(2^3)^2 = 2^{3 \times 2} = 2^6 = 64
\]
In this example:
- First, you raised 2 to the power of 3, which gives 8.
- Then, you squared 8, or \( 8^2 = 64 \).
So, the "power of a power" rule helps simplify expressions like this by multiplying the exponents.