Calculate (16×2×3)¹¹: Solving a Compound Exponential Expression

To solve the expression $\left(16\times2\times3\right)^{11}$, we will use the Power of a Product rule. According to this rule, when you have a product raised to an exponent, you can distribute the exponent to each factor in the product. Mathematically, this is expressed as:

$(a \times b \times c)^n = a^n \times b^n \times c^n$

• In our expression, $a = 16$, $b = 2$, and $c = 3$.

Applying the Power of a Product formula to our expression gives:

$(16 \times 2 \times 3)^{11} = 16^{11} \times 2^{11} \times 3^{11}$

This shows that each factor inside the parentheses is raised to the power of 11, which is consistent with the provided answer:

$16^{11}\times2^{11}\times3^{11}$