power rule of exponents

The power rule says that raising a power to another power multiplies the exponents: (b^m)^n = b^(m×n). You are taking n copies of the inner power, and each copy contributes m factors, so altogether there are m × n factors.

Consider (2^3)^2. The inner part 2^3 is one block of three 2s; squaring it means using two such blocks, 2^3 × 2^3, which is six 2s, namely 2^6. Multiplying 3 × 2 = 6 gives the total directly.

This rule is easy to confuse with the product rule. When you multiply like bases you add exponents; when you raise a power to a power you multiply them. Also note (ab)^n = a^n b^n distributes over a product, but (a + b)^n does not split that way — a frequent and costly error.