Questions: Simplify. [ (8 v^4 u^3)^2 ] Write your answer without parentheses.

Transcript text: Module 4 Homework 4.1 - Properties of Exponen Question 7 of 15 (1 point) I Question Atte 1 $\checkmark 2$ 3 Simplify. \[ \left(8 v^{4} u^{3}\right)^{2} \] Write your answer without parentheses. $\square$ Check

Solution

Solution Steps

To simplify the given expression $(8v^4u^3)^2$, we need to apply the power of a product rule, which states that $(ab)^n = a^n b^n$. This means we will raise each factor inside the parentheses to the power of 2.

Step 1: Apply the Power of a Product Rule

The power of a product rule states that $(ab)^n = a^n b^n$. We apply this rule to each term inside the parentheses: \[ \left(8 v^{4} u^{3}\right)^{2} = 8^2 \left(v^{4}\right)^2 \left(u^{3}\right)^2 \]

Step 2: Simplify Each Term

Next, we simplify each term separately: \[ 8^2 = 64 \] \[ \left(v^{4}\right)^2 = v^{4 \cdot 2} = v^{8} \] \[ \left(u^{3}\right)^2 = u^{3 \cdot 2} = u^{6} \]

Step 3: Combine the Simplified Terms

Now, we combine all the simplified terms: \[ 64 v^{8} u^{6} \]