What will come in place of question mark (?) .
`(10)^(0.25) xx (10)^(0.50) xx 10^(0.100)= ?`

Options

A. `10^(20//17)`
B. `10^(17//20)`
C. `10^(5//17)`
D. `10^(33)`

Answer

To solve the expression \( (10)^{0.25} \times (10)^{0.50} \times (10)^{0.100} \), we can use the property of exponents that states when multiplying like bases, we add the exponents.

### Step 1: Write down the expression
We start with the expression:
\[ (10)^{0.25} \times (10)^{0.50} \times (10)^{0.100} \]

### Step 2: Apply the property of exponents
Using the property of exponents:
\[ a^m \times a^n = a^{m+n} \]
we can combine the exponents:
\[ 10^{0.25 + 0.50 + 0.100} \]

### Step 3: Calculate the sum of the exponents
Now, we need to add the exponents. First, we convert each exponent to have a common denominator. The denominators are 4, 2, and 10. The least common multiple (LCM) of these numbers is 20.

Convert each exponent:
- \( 0.25 = \frac{1}{4} = \frac{5}{20} \)
- \( 0.50 = \frac{1}{2} = \frac{10}{20} \)
- \( 0.100 = \frac{1}{10} = \frac{2}{20} \)

Now we can add them:
\[ \frac{5}{20} + \frac{10}{20} + \frac{2}{20} = \frac{5 + 10 + 2}{20} = \frac{17}{20} \]

### Step 4: Write the final expression
Now we substitute back into the expression:
\[ 10^{\frac{17}{20}} \]

### Conclusion
The value that comes in place of the question mark is:
\[ 10^{\frac{17}{20}} \]