`(1""3/4)^(3)=?`

Options

A. `1""(27)/(64)`
B. `2""(27)/(64)`
C. `5""(23)/(64)`
D. None of these

Answer

To solve the question \((1 \frac{3}{4})^3\), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \(1 \frac{3}{4}\) can be converted to an improper fraction.

To do this, multiply the whole number (1) by the denominator (4) and add the numerator (3):

\[ 1 \times 4 + 3 = 4 + 3 = 7 \]

So, \(1 \frac{3}{4} = \frac{7}{4}\).

### Step 2: Cube the improper fraction
Now, we need to cube the improper fraction \(\frac{7}{4}\):

\[ \left(\frac{7}{4}\right)^3 = \frac{7^3}{4^3} \]

Calculating \(7^3\) and \(4^3\):

\[ 7^3 = 7 \times 7 \times 7 = 343 \]
\[ 4^3 = 4 \times 4 \times 4 = 64 \]

So,

\[ \left(\frac{7}{4}\right)^3 = \frac{343}{64} \]

### Step 3: Express the result as a mixed fraction
Now, we need to express \(\frac{343}{64}\) as a mixed fraction.

To do this, divide 343 by 64:

\[ 343 \div 64 = 5 \quad \text{(since \(64 \times 5 = 320\))} \]

Now, find the remainder:

\[ 343 - 320 = 23 \]

Thus, we can express \(\frac{343}{64}\) as:

\[ 5 \frac{23}{64} \]

### Final Answer
Therefore, the final answer is:

\[ (1 \frac{3}{4})^3 = 5 \frac{23}{64} \]