Solve ((4×3)³)⁶: Nested Exponents with Order of Operations

To solve this problem, we'll apply the power of a power rule on the expression $((4 \times 3)^3)^6$.

Here's how we proceed:

• Step 1: Identify the expression
  The expression given is $((4 \times 3)^3)^6$.

• Step 2: Apply the Power of a Power Rule
  According to the power of a power rule, $(a^m)^n = a^{m \times n}$.
  Therefore, $((4 \times 3)^3)^6 = (4 \times 3)^{3 \times 6}$.

• Step 3: Calculate the Exponent Product
  Multiply the exponents: $3 \times 6 = 18$.

• Step 4: Simplify the Expression
  Thus, we have $(4 \times 3)^{18}$.

Therefore, the simplified expression is $(4 \times 3)^{18}$.

Comparing with the choices provided:

• Choice 1: $(4 \times 3)^2$ - Incorrect.

• Choice 2: $(4 \times 3)^3$ - Incorrect.

• Choice 3: $(4 \times 3)^{18}$ - Correct.

• Choice 4: $(4 \times 3)^{-3}$ - Incorrect.

Thus, the correct answer is: $(4 \times 3)^{18}$, which corresponds to choice 3