If you raise a power to another power, what do you do with the exponents?

If you raise a power to another power, what do you do with the exponents?

• A. Add the exponents
• B. Multiply the exponents
• C. Divide the exponents
• D. Keep exponents the same

Answer: (B)

When you raise a power to another power, you multiply the exponents. The rule is (a^m)^n = a^{m n}. For example, (3^4)^2 equals 3^8, which is 6561, and (x^5)^2 equals x^{10}. This works because repeating the multiplication inside the base means you apply the exponent to each factor in the product, adding up how many times the base is multiplied. The other options don’t fit because they would correspond to different situations: adding exponents happens when you multiply expressions with the same base (a^m · a^n), not when you nest powers; dividing or keeping exponents the same wouldn’t reflect the repeated multiplication inside the parentheses.

When you raise a power to another power, you multiply the exponents. The rule is (a^m)^n = a^{m n}. For example, (3^4)^2 equals 3^8, which is 6561, and (x^5)^2 equals x^{10}. This works because repeating the multiplication inside the base means you apply the exponent to each factor in the product, adding up how many times the base is multiplied. The other options don’t fit because they would correspond to different situations: adding exponents happens when you multiply expressions with the same base (a^m · a^n), not when you nest powers; dividing or keeping exponents the same wouldn’t reflect the repeated multiplication inside the parentheses.