Find the cube-roots of :
`64xx729`

Answer

To find the cube root of the number \( 64 \times 729 \), we can follow these steps:

### Step 1: Define the number
Let \( A = 64 \times 729 \).

### Step 2: Write the expression for the cube root
We need to find \( A^{1/3} \).

### Step 3: Substitute the value of \( A \)
Substituting the value of \( A \) into the expression gives us:
\[ A^{1/3} = (64 \times 729)^{1/3} \]

### Step 4: Factor the numbers
We can factor \( 64 \) and \( 729 \):
- \( 64 = 4^3 \) (since \( 4 \times 4 \times 4 = 64 \))
- \( 729 = 9^3 \) (since \( 9 \times 9 \times 9 = 729 \))

### Step 5: Rewrite the expression using the factors
Now we can rewrite the expression as:
\[ (4^3 \times 9^3)^{1/3} \]

### Step 6: Apply the property of exponents
Using the property \( (a^m \times b^m) = (a \times b)^m \), we can simplify:
\[ (4 \times 9)^3^{1/3} \]

### Step 7: Simplify the exponent
Now, using the property \( (a^m)^n = a^{m \cdot n} \):
\[ (4 \times 9)^{3 \cdot \frac{1}{3}} = (4 \times 9)^1 \]

### Step 8: Calculate the multiplication
Now calculate \( 4 \times 9 \):
\[ 4 \times 9 = 36 \]

### Final Answer
Thus, the cube root of \( 64 \times 729 \) is:
\[ \boxed{36} \]

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