The problem asks to identify the property demonstrated by the equation: $\pi * (-\frac{1}{\sqrt{5}} * -\sqrt{5}) = \pi * 1$. The possible properties are additive identity, additive inverse, multiplicative identity, and multiplicative inverse.

1. Problem Description

The problem asks to identify the property demonstrated by the equation: $\pi * (-\frac{1}{\sqrt{5}} * -\sqrt{5}) = \pi * 1$. The possible properties are additive identity, additive inverse, multiplicative identity, and multiplicative inverse.

2. Solution Steps

First, let's simplify the expression inside the parentheses:

$-\frac{1}{\sqrt{5}} * -\sqrt{5}$.

A negative number times a negative number is a positive number. Thus, we have:

$\frac{1}{\sqrt{5}} * \sqrt{5} = \frac{\sqrt{5}}{\sqrt{5}}$.

Since any non-zero number divided by itself is equal to 1:

$\frac{\sqrt{5}}{\sqrt{5}} = 1$.

So the equation becomes:

$\pi * (1) = \pi * 1$.

$\pi = \pi$

This shows that multiplying $\pi$ by 1 results in $\pi$. This demonstrates the multiplicative identity property. However, the original equation also shows that $-\frac{1}{\sqrt{5}} * -\sqrt{5}=1$. In general, if the product of two numbers equals to 1, then they are multiplicative inverses.

The equation shows that $-\frac{1}{\sqrt{5}}$ and $-\sqrt{5}$ are multiplicative inverses of each other since their product equals

1. So, the initial equation is showing the multiplicative inverse property.

3. Final Answer

(d) Multiplicative Inverse