Compute (x^3)^4.

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Multiple Choice

Compute (x^3)^4.

Explanation:
Raising a power to another power multiplies the exponents: (x^3)^4 = x^{3·4} = x^{12}. This uses the rule (a^m)^n = a^{mn}, valid for any x (with standard conventions for zero and negative exponents). So the expression simplifies to x^{12}. The other forms come from mixing up the operations: x^7 would come from multiplying x^3 by x^4, not from taking a power of a power; 4x^3 is treating the exponent as if it distributes to the coefficient; x^{-12} would come from a different setup, such as taking the reciprocal after a negative exponent.

Raising a power to another power multiplies the exponents: (x^3)^4 = x^{3·4} = x^{12}. This uses the rule (a^m)^n = a^{mn}, valid for any x (with standard conventions for zero and negative exponents).

So the expression simplifies to x^{12}. The other forms come from mixing up the operations: x^7 would come from multiplying x^3 by x^4, not from taking a power of a power; 4x^3 is treating the exponent as if it distributes to the coefficient; x^{-12} would come from a different setup, such as taking the reciprocal after a negative exponent.

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