# How do you multiply (\frac { 2x } { 5} ) ^ { 2} \cdot ( \frac { 5} { x } ) ^ { 2} ?

Feb 22, 2017

$4$

#### Explanation:

Before we multiply, let's simplify each individual term.

${\left(\frac{2 x}{5}\right)}^{2} \cdot {\left(\frac{5}{x}\right)}^{2}$

Each term can be simplified since they are being squared.

$\left(\frac{2 x}{5}\right) \left(\frac{2 x}{5}\right) \cdot \left(\frac{5}{x}\right) \left(\frac{5}{x}\right)$

SImplify each term.

$\left(\frac{2 x \cdot 2 x}{5 \cdot 5}\right) \cdot \left(\frac{5 \cdot 5}{x \cdot x}\right)$

Simplify further.

$\left(\frac{4 {x}^{2}}{25}\right) \cdot \left(\frac{25}{x} ^ 2\right)$

Now we can multiply. Let's simplify across the numerators and denominators first.

$\frac{4 \cancel{{x}^{2}}}{25} \cdot \frac{25}{{\cancel{x}}^{2}}$

Now we get:

$\frac{4}{25} \cdot \frac{25}{1}$

This can still be simplified.

$\frac{4}{\cancel{25}} \cdot \frac{\cancel{25}}{1}$

$= \frac{4}{1}$

Now rewrite.

$4$