`(8)^(2//3)`=?`

Options

A. `sqrt4`
B. 2
C. 4
D. 64

Answer

To solve the expression \( (8)^{\frac{2}{3}} \), we can follow these steps:

### Step 1: Rewrite the base
First, we can express 8 as a power of 2. We know that:
\[ 8 = 2^3 \]
So we can rewrite the expression:
\[ (8)^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} \]

### Step 2: Apply the power of a power rule
Using the power of a power rule, which states that \( (a^m)^n = a^{m \cdot n} \), we can simplify the expression:
\[ (2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} \]

### Step 3: Simplify the exponent
Now we can simplify the exponent:
\[ 3 \cdot \frac{2}{3} = 2 \]
So we have:
\[ 2^{3 \cdot \frac{2}{3}} = 2^2 \]

### Step 4: Calculate the final value
Now we can calculate \( 2^2 \):
\[ 2^2 = 4 \]

Thus, the final answer is:
\[ (8)^{\frac{2}{3}} = 4 \]