### Instruction: Find $\left(\frac{5}{7}\right)^{3}\left(\frac{4}{5}\right)^{3}$.### Response: To simplify this expression, I can use the property of exponents that says $(a/b)^c = a^c / b^c$.
So, I can rewrite the expression as $\frac{5^3}{7^3} \cdot \frac{4^3}{5^3}$.
Now, I can use the property of fractions that says $\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$.
So, I can multiply the numerators and the denominators of the fractions and get $\frac{5^3 \cdot 4^3}{7^3 \cdot 5^3}$.
I notice that $5^3$ appears in both the numerator and the denominator, so I can cancel them out and get $\frac{4^3}{7^3}$.
To evaluate this fraction, I need to cube 4 and 7 and get $\frac{64}{343}$.
This is the simplest form of the expression, so I am done.