Find the cubes of :
`8/9`

Answer

To find the cube of the fraction \( \frac{8}{9} \), we will follow these steps:

### Step 1: Write the expression for the cube
The cube of a number \( x \) is given by \( x^3 \). Therefore, the cube of \( \frac{8}{9} \) can be written as:
\[ \left(\frac{8}{9}\right)^3 \]

### Step 2: Apply the cube to the numerator and denominator
Using the property of exponents, we can cube the numerator and the denominator separately:
\[ \left(\frac{8}{9}\right)^3 = \frac{8^3}{9^3} \]

### Step 3: Calculate \( 8^3 \)
Now we need to calculate \( 8^3 \):
\[ 8^3 = 8 \times 8 \times 8 \]
Calculating this step by step:
- First, \( 8 \times 8 = 64 \)
- Then, \( 64 \times 8 = 512 \)

So, \( 8^3 = 512 \).

### Step 4: Calculate \( 9^3 \)
Next, we calculate \( 9^3 \):
\[ 9^3 = 9 \times 9 \times 9 \]
Calculating this step by step:
- First, \( 9 \times 9 = 81 \)
- Then, \( 81 \times 9 = 729 \)

So, \( 9^3 = 729 \).

### Step 5: Combine the results
Now we can combine the results from steps 3 and 4:
\[ \left(\frac{8}{9}\right)^3 = \frac{512}{729} \]

### Final Answer
Thus, the cube of \( \frac{8}{9} \) is:
\[ \frac{512}{729} \]

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