find the volume of the rectangular prism. write your answer in simplest form.

Explanation:

Step1: Recall volume formula

The volume $V$ of a rectangular - prism is $V = l\times w\times h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Identify dimensions

Let $l=\frac{4}{7}\text{ cm}$, $w = \frac{1}{5}\text{ cm}$, and $h=\frac{7}{9}\text{ cm}$.

Step3: Calculate volume

$V=\frac{4}{7}\times\frac{1}{5}\times\frac{7}{9}$ First, multiply $\frac{4}{7}$ and $\frac{1}{5}$: $\frac{4}{7}\times\frac{1}{5}=\frac{4\times1}{7\times5}=\frac{4}{35}$. Then, multiply $\frac{4}{35}$ by $\frac{7}{9}$: $\frac{4}{35}\times\frac{7}{9}=\frac{4\times7}{35\times9}=\frac{28}{315}$. Simplify $\frac{28}{315}$ by dividing both the numerator and denominator by 7: $\frac{28\div7}{315\div7}=\frac{4}{45}$.

Answer:

$\frac{4}{45}\text{ cm}^3$