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

Question

Choose the expression that corresponds to the following:

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

00:08 Let's simplify the expression together.

00:14 To open parentheses with an exponent, especially when there's multiplication involved,

00:20 we raise each factor inside to the power separately.

00:24 We'll apply this formula to solve our problem.

00:32 And here is how we find the solution. Great job!

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

$2^5\times11^5$