Calculate (2×11)^5: Evaluating Powers of Products

Question

Choose the expression that corresponds to the following:

$\left(2\times11\right)^5=$

00:00 Simplify the following expression

00:06 In order to open parentheses with an exponent which contain a multiplication operation

00:10 Raise each factor to the power

00:16 We will use this formula in our exercise

00:24 This is the solution

To solve the expression, we can apply the rule for the power of a product, which states that $\left(a \times b\right)^n = a^n \times b^n$ .

In this case, our expression is $\left(2\times11\right)^5$ , where $a = 2$ and $b = 11$ , and $n = 5$ .

Applying the power of a product rule gives us:

Therefore, $\left(2\times11\right)^5 = 2^5 \times 11^5$ .

$2^5\times11^5$