Multiply Powers: 16^23 × 17^23 × 2^23 × 8^23 × 4^23 Expression

Insert the corresponding expression:

$16^{23}\times17^{23}\times2^{23}\times8^{23}\times4^{23}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

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

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

00:12 This formula is valid regardless of how many factors are in the product

00:18 We will apply this formula to our exercise

00:24 We'll break down the product into each factor separately raised to the power (N)

00:34 This is the solution

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Recognize the common power in the expression.
The given expression is $16^{23} \times 17^{23} \times 2^{23} \times 8^{23} \times 4^{23}$ .
Step 2: Apply the power of a product rule.
According to the exponent rule $a^n \times b^n = (a \times b)^n$ , terms raised to the same power can be combined.
Therefore, combine the terms inside a single power: $(16 \times 17 \times 2 \times 8 \times 4)^{23}$ .

The correct answer from the given choices is: Choice 2: $\left(16 \times 17 \times 2 \times 8 \times 4\right)^{23}$ .