Simplify (x³)⁴: Solving Compound Exponent Expression

To simplify the expression $(x^3)^4$, we'll follow these steps:

• Step 1: Identify the expression: $(x^3)^4$.
• Step 2: Apply the formula for a power raised to another power.
• Step 3: Calculate the product of the exponents.

Now, let's work through each step:

Step 1: We have the expression $(x^3)^4$, which involves a power raised to another power.

Step 2: We apply the exponent rule $(a^m)^n = a^{m \cdot n}$ here with $a = x$, $m = 3$, and $n = 4$.

Step 3: Multiply the exponents: $3 \times 4 = 12$. This gives us a new exponent for the base $x$.

Therefore, $(x^3)^4 = x^{12}$.

Consequently, the correct answer choice is: $x^{12}$ from the options provided. The other options $x^6$, $x^1$, and $x^7$ do not reflect the correct application of the exponent multiplication rule.