Evaluate the following:
`(20/7)^3`

Answer

To evaluate the expression \((\frac{20}{7})^3\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \left(\frac{20}{7}\right)^3 \]

### Step 2: Apply the power to the numerator and denominator
Using the property of exponents \((\frac{a}{b})^n = \frac{a^n}{b^n}\), we can rewrite the expression as:
\[ \frac{20^3}{7^3} \]

### Step 3: Calculate \(20^3\)
Now, we need to calculate \(20^3\):
\[ 20^3 = 20 \times 20 \times 20 \]
Calculating this step-by-step:
- First, calculate \(20 \times 20 = 400\).
- Then, multiply \(400 \times 20 = 8000\).
So, \(20^3 = 8000\).

### Step 4: Calculate \(7^3\)
Next, we calculate \(7^3\):
\[ 7^3 = 7 \times 7 \times 7 \]
Calculating this step-by-step:
- First, calculate \(7 \times 7 = 49\).
- Then, multiply \(49 \times 7 = 343\).
So, \(7^3 = 343\).

### Step 5: Combine the results
Now, we can substitute back into our fraction:
\[ \frac{20^3}{7^3} = \frac{8000}{343} \]

### Step 6: Final result
Thus, the evaluated expression is:
\[ \left(\frac{20}{7}\right)^3 = \frac{8000}{343} \]