Calculate (10×11×20×4×9)^8: Solving Multi-Factor Exponential Expression

Question

Insert the corresponding expression:

$\left(10\times11\times20\times4\times9\right)^8=$

00:11 Let's simplify this problem.

00:15 According to the laws of exponents, when a product is raised to a power, let's call it N,

00:21 it equals each factor separately raised to the power of N.

00:25 This formula works no matter how many factors there are in the product.

00:37 Let's apply this formula to our exercise.

00:41 We will break down each part and raise it to the power of N.

00:50 And that's how we solve this problem!

To solve this problem, we'll apply the power of a product rule for exponents:

Given the expression:

$\left(10 \times 11 \times 20 \times 4 \times 9\right)^8$

According to the power of a product rule, which states that $(a \times b)^n = a^n \times b^n$ , we can expand this expression:

$\left(10^8 \times 11^8 \times 20^8 \times 4^8 \times 9^8\right)$

Therefore, the corresponding expanded expression is:

$10^8 \times 11^8 \times 20^8 \times 4^8 \times 9^8$

$10^8\times11^8\times20^8\times4^8\times9^8$