Evaluate `(4/7)^(3)`

Options

A. `(4/7)^(3)`
B. `((10)/(11))^(3)`
C. `(1/(15))^(3)`
D. `(1""3/(10))^(3)`

Answer

To evaluate \((\frac{4}{7})^3\), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \left(\frac{4}{7}\right)^3 \]

### Step 2: Apply the power to the numerator and denominator
According to the rules of exponents, we can apply the exponent to both the numerator and the denominator:
\[ \left(\frac{4}{7}\right)^3 = \frac{4^3}{7^3} \]

### Step 3: Calculate \(4^3\)
Now we calculate \(4^3\):
\[ 4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64 \]

### Step 4: Calculate \(7^3\)
Next, we calculate \(7^3\):
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]

### Step 5: Write the final result
Now we can write the final result:
\[ \left(\frac{4}{7}\right)^3 = \frac{64}{343} \]

Thus, the evaluated answer is:
\[ \frac{64}{343} \]

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