Problem 43 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(-3 x^{2} y^{5}\right)^{2}$$

Step-by-Step Solution

Answer

The simplified form of \((-3 x^{2} y^{5})^{2}\) is \(9 * x^{4} * y^{10}\)

Step 1: Apply Exponent Rule

Follow the exponent rule that says \((ab)^n = a^n * b^n\). Let's apply this rule to \( (-3 x^{2} y^{5})^{2} \). This rule allows us to separately apply the square to each part of the expression within the parenthesis. Doing so, we get: \[ (-3)^{2} * (x^{2})^{2} * (y^{5})^{2} \]

Step 2: Calculate Each Part

Evaluate each part of the expression separately. The square of -3 is 9. Applying the rule that says \((a^n)^m = a^(n*m)\), we get \(x^{2*2}\) and \(y^{5*2}\). Calculate these to simplify the expression to: \[ 9 * x^{4} * y^{10} \]