Solve ((4×6)³)⁴: Calculating Nested Exponents Step-by-Step

To solve this problem, we'll use the power of a power property of exponents, which states that for any base $a$ and exponents $m$ and $n$, $(a^m)^n = a^{m \times n}$.

• Step 1: Identify the base and exponents:
  In the given expression $\left(\left(4 \times 6\right)^3\right)^4$, the base is $(4 \times 6)$, the inner exponent is 3, and the outer exponent is 4.

• Step 2: Apply the power of a power rule:
  According to the rule, $\left((4 \times 6)^3\right)^4$ simplifies to $(4 \times 6)^{3 \times 4}$.

• Step 3: Calculate the new exponent:
  Multiply the exponents: $3 \times 4 = 12$. Hence, the expression simplifies to $(4 \times 6)^{12}$.

The expression $\left(\left(4 \times 6\right)^3\right)^4$ is equivalent to $(4 \times 6)^{3 \times 4}$. Therefore, the correct choice is:

$\left(4\times6\right)^{3\times4}$

Therefore, the correct answer is Choice 1.