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

Question

Insert the corresponding expression:

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

00:00 Simplify the following problem

00:04 According to the laws of exponents, a product that is raised to a power (N)

00:08 equals a product where each factor is raised to the same power (N)

00:14 This formula is valid regardless of how many factors are in the product

00:26 We will apply this formula to our exercise

00:29 We will break down the product into each factor separately raised to the power (N)

00:39 This is the solution

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:

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

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