What approximate value should come in place of the questions mark (?) in the following questions ? (You are not expected to calculate the exact value )
`8^(1.38) xx 8^(1.63) = ?`

Options

A. 680
B. 218
C. 726
D. 512

Answer

To solve the problem \( 8^{1.38} \times 8^{1.63} = ? \), we can use the property of exponents that states:

\[ a^m \times a^n = a^{m+n} \]

### Step 1: Combine the exponents
Using the property mentioned above, we can combine the exponents of the base 8:

\[ 8^{1.38} \times 8^{1.63} = 8^{(1.38 + 1.63)} \]

### Step 2: Calculate the sum of the exponents
Now, we need to add the exponents:

\[ 1.38 + 1.63 = 3.01 \]

### Step 3: Rewrite the expression
Now we can rewrite the expression as:

\[ 8^{3.01} \]

### Step 4: Approximate the value of \( 8^{3.01} \)
To find an approximate value for \( 8^{3.01} \), we can use the fact that \( 8^3 = 512 \). Since \( 3.01 \) is slightly greater than \( 3 \), we can estimate that:

\[ 8^{3.01} \approx 512 \]

### Conclusion
Thus, the approximate value that should come in place of the question mark (?) is:

\[ \boxed{512} \]