Solve: Product of Powers 20¹¹ × 4¹¹ × 2¹¹ × 5¹¹ × 3¹¹

Insert the corresponding expression:

$20^{11}\times4^{11}\times2^{11}\times5^{11}\times3^{11}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the power laws, a product raised to a power (N)

00:07 Equals a product where each factor is raised to that same power (N)

00:10 This formula is valid regardless of how many factors are in the product

00:25 We will apply this formula to our exercise

00:30 We'll break down the product into each factor separately raised to the power (N)

00:45 This is the solution

Step-by-Step Solution

To solve this problem, we will use the rule of exponents which allows us to simplify expressions of the form $a^n \times b^n = (a \times b)^n$ .

Here's how to simplify the expression step by step:

Step 1: Start with the original expression: $20^{11} \times 4^{11} \times 2^{11} \times 5^{11} \times 3^{11}$ .
Step 2: Recognize that each term (20, 4, 2, 5, and 3) is raised to the power of 11, which allows the use of the product of powers rule. We can combine these bases into a single base raised to the common power: $(20 \times 4 \times 2 \times 5 \times 3)^{11}$

Hence, the expression simplifies to $\left(20 \times 4 \times 2 \times 5 \times 3\right)^{11}$ , which corresponds to choice 3.