We are asked to evaluate the expression $\sqrt[6]{15625}$. This means we need to find a number which, when raised to the power of 6, equals 15625.

1. Problem Description

We are asked to evaluate the expression $\sqrt[6]{15625}$. This means we need to find a number which, when raised to the power of 6, equals

1

5

6

2

5.

2. Solution Steps

We want to find $x$ such that $x^6 = 15625$.

We can start by finding the prime factorization of

1

5

6

2

5. $15625 = 5 \times 3125 = 5 \times 5 \times 625 = 5 \times 5 \times 5 \times 125 = 5 \times 5 \times 5 \times 5 \times 25 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5^6$.

So, we have $\sqrt[6]{15625} = \sqrt[6]{5^6}$.

Since the root and the power are the same, we can simplify this to $5$.

3. Final Answer

The final answer is 5.