What will come in place of both the question marks (?) in the following questions ?
`((?)^(2.7))/(98)=((28))/((?)^(0.3))`

Options

A. 7
B. 14
C. 8
D. 12

Answer

To solve the equation \(\frac{(?)^{2.7}}{98} = \frac{28}{(?)^{0.3}}\), we will follow these steps:

1. **Substitute the question mark with a variable**:
Let \( x = ? \). Thus, the equation becomes:
\[ \frac{x^{2.7}}{98} = \frac{28}{x^{0.3}} \]

2. **Cross-multiply to eliminate the fractions**:
\[ x^{2.7} \cdot x^{0.3} = 28 \cdot 98 \]

3. **Combine the powers of \( x \)**:
Using the property of exponents \( a^m \cdot a^n = a^{m+n} \):
\[ x^{2.7 + 0.3} = 28 \cdot 98 \]
Simplifying the left side:
\[ x^{3} = 28 \cdot 98 \]

4. **Calculate \( 28 \cdot 98 \)**:
First, we can factor \( 28 \) and \( 98 \):
\[ 28 = 2^2 \cdot 7 \quad \text{and} \quad 98 = 2 \cdot 7^2 \]
Therefore,
\[ 28 \cdot 98 = (2^2 \cdot 7) \cdot (2 \cdot 7^2) = 2^{2+1} \cdot 7^{1+2} = 2^3 \cdot 7^3 \]

5. **Set the equation**:
Now we have:
\[ x^3 = 2^3 \cdot 7^3 \]

6. **Take the cube root of both sides**:
\[ x = 2 \cdot 7 = 14 \]

Thus, the value that comes in place of both question marks is \( 14 \).