Calculate (11×15×4)^6: Solving a Complex Exponent Problem

Choose the expression that corresponds to the following:

$\left(11\times15\times4\right)^6=$

The expression in question is $(11 \times 15 \times 4)^6$.

Using the power of a product rule, we know that any numbers $a$, $b$, and $c$ can be written as$(a \times b \times c)^n = a^n \times b^n \times c^n$.

Applying this, we get:

$(11 \times 15 \times 4)^6 = 11^6 \times 15^6 \times 4^6$

Verify the multiple-choice options:
- Option 1: Clearly represents the expression as $11^6 \times 15^6 \times 4^6$, so this is correct.
- Option 2: If we combine $15 \times 4 = 60$, the expression becomes $(11 \times 60)^6$, which matches $11^6 \times 60^6$, therefore correct.
- Option 3: If we combine $11 \times 4 = 44$, the expression becomes $(44 \times 15)^6$, which aligns with $44^6 \times 15^6$, therefore correct.

Since all three expressions are validated as equivalent to the original expression when simplified appropriately, all answers are correct.