`8^(4//3) xx 2^(-1) =`

Options

A. 4
B. 8
C. 16
D. 32

Answer

To solve the expression \( 8^{\frac{4}{3}} \times 2^{-1} \), we can follow these steps:

### Step 1: Rewrite the base 8 in terms of base 2
We know that \( 8 = 2^3 \). Therefore, we can rewrite \( 8^{\frac{4}{3}} \) as:
\[ (2^3)^{\frac{4}{3}} \]

### 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:
\[ (2^3)^{\frac{4}{3}} = 2^{3 \cdot \frac{4}{3}} = 2^4 \]

### Step 3: Substitute back into the expression
Now we substitute \( 2^4 \) back into the original expression:
\[ 2^4 \times 2^{-1} \]

### Step 4: Apply the product of powers rule
Using the product of powers rule, which states that \( a^m \times a^n = a^{m+n} \), we can combine the exponents:
\[ 2^4 \times 2^{-1} = 2^{4 + (-1)} = 2^{4 - 1} = 2^3 \]

### Step 5: Calculate the final value
Now, we can calculate \( 2^3 \):
\[ 2^3 = 8 \]

Thus, the value of the expression \( 8^{\frac{4}{3}} \times 2^{-1} \) is \( 8 \).

---