The problem asks to select all ratios that are equivalent to the ratio $7:21$. The given ratios are $5:15$, $2:9$, and $108:105$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $7:21$. The given ratios are $5:15$, $2:9$, and $108:105$.

2. Solution Steps

First, simplify the ratio $7:21$.

$$$$

\frac{7}{21} = \frac{7 \div 7}{21 \div 7} = \frac{1}{3}

$$$$

So, the simplified form of the ratio $7:21$ is $1:3$.

Now, we check each of the given ratios:

Ratio 1: $5:15$

$$$$

\frac{5}{15} = \frac{5 \div 5}{15 \div 5} = \frac{1}{3}

$$$$

Since $\frac{5}{15} = \frac{1}{3}$, the ratio $5:15$ is equivalent to $7:21$.

Ratio 2: $2:9$

$$$$

\frac{2}{9}

$$$$

Since $\frac{2}{9}$ cannot be simplified further and is not equal to $\frac{1}{3}$, the ratio $2:9$ is not equivalent to $7:21$.

Ratio 3: $108:105$

$$$$

\frac{108}{105} = \frac{108 \div 3}{105 \div 3} = \frac{36}{35}

$$$$

Since $\frac{36}{35}$ is not equal to $\frac{1}{3}$, the ratio $108:105$ is not equivalent to $7:21$.

3. Final Answer

The only ratio equivalent to $7:21$ among the given options is $5:15$.