Find the cube-roots of :
729

Answer

To find the cube root of 729, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number**: We need to find the cube root of 729. We denote this as \( a = 729 \).

2. **Use the cube root formula**: The cube root of a number can be expressed mathematically as \( a^{1/3} \). Therefore, we write:
\[ \text{Cube root of } 729 = 729^{1/3} \]

3. **Express 729 as a power**: We need to express 729 in terms of a base raised to an exponent. We know that:
\[ 729 = 9^3 \]
So we can rewrite our expression:
\[ 729^{1/3} = (9^3)^{1/3} \]

4. **Apply the power of a power rule**: According to the power of a power rule, \( (a^m)^n = a^{m \cdot n} \). Thus, we can simplify:
\[ (9^3)^{1/3} = 9^{3 \cdot (1/3)} = 9^1 \]

5. **Calculate the final value**: Since \( 9^1 = 9 \), we conclude that:
\[ 729^{1/3} = 9 \]

6. **Final answer**: Therefore, the cube root of 729 is:
\[ \text{Cube root of } 729 = 9 \]