According to the Power Rule, what is (x^4)^3 equal to?

According to the Power Rule, what is (x^4)^3 equal to?

• A. x^7
• B. x^12
• C. x^43
• D. x^1

Answer: (B)

When you raise a power to another power, you multiply the exponents. So (x^4)^3 becomes x^(4×3) = x^12. This works because you’re applying the same base x repeatedly: four x’s raised to the third power means you have twelve x’s in total. If you added exponents, you’d be multiplying x^4 by x^3 and would get x^7, which isn’t the same operation. The result here is x^12.

When you raise a power to another power, you multiply the exponents. So (x^4)^3 becomes x^(4×3) = x^12. This works because you’re applying the same base x repeatedly: four x’s raised to the third power means you have twelve x’s in total. If you added exponents, you’d be multiplying x^4 by x^3 and would get x^7, which isn’t the same operation. The result here is x^12.