To solve $1 \times \left(\frac{4}{5}\right)^3$, let's follow these steps:

Step 1: Calculate $\left(\frac{4}{5}\right)^3$

$\left(\frac{4}{5}\right)^3 = \frac{4^3}{5^3} = \frac{64}{125}$

Step 2: Multiply by 1

Since multiplying by 1 does not change the value: $1 \times \frac{64}{125} = \frac{64}{125}$

Thus, the result is: $\frac{64}{125}$

Would you like more details on any step or have additional questions?

Here are 5 related questions to deepen your understanding:

1. How do you convert a fraction to a decimal?
2. What happens when you raise a fraction to a negative exponent?
3. How do you simplify expressions involving powers of fractions?
4. Can you express $\frac{64}{125}$ as a percentage?
5. How do you calculate $\left(\frac{a}{b}\right)^n$ for any values of $a$, $b$, and $n$?

Tip: Always simplify fractions and perform any power operations before applying other arithmetic operations.