Problem 97 - College Algebra

Question

Simplify using properties of exponents. $$\left(25 x^{4} y^{6}\right)^{\frac{1}{2}}$$

Step-by-Step Solution

Answer

The simplified expression is \(5x^{2}y^{3}\).

Step 1: Identify the expression

The expression given is \( \left(25 x^{4} y^{6}\right)^{\frac{1}{2}} \). This can be separated into three separate terms -- \(25^{\frac{1}{2}}\), \(x^{4*\frac{1}{2}}\), and \(y^{6*\frac{1}{2}}\).

Step 2: Apply properties of exponents

Now, apply the properties of exponents to each term. \(25^{\frac{1}{2}}\) is the square root of 25, which gives 5. Also, multiply the exponents in \(x^{4*\frac{1}{2}}\) and \(y^{6*\frac{1}{2}}\), which gives \(x^{2}\) and \(y^{3}\) respectively.

Step 3: Combine terms

Putting these terms together will yield the final simplified expression, which is \(5x^{2}y^{3}\).