`95^(3//7)*95^(0.89) = 95^(?)`

Options

A. a. 1.31
B. b. 3
C. c. 2.99
D. d. 2.7

Answer

To solve the equation \( 95^{\frac{3}{7}} \times 95^{0.89} = 95^{?} \), we can use the property of exponents which states that when multiplying two powers with the same base, we can add their exponents.

### Step-by-step Solution:

1. **Identify the Base and Exponents**:
- The base is \( 95 \).
- The exponents are \( \frac{3}{7} \) and \( 0.89 \).

2. **Apply the Exponent Addition Rule**:
- According to the property of exponents, we can combine the exponents:
\[ 95^{\frac{3}{7}} \times 95^{0.89} = 95^{\left(\frac{3}{7} + 0.89\right)} \]

3. **Convert \( 0.89 \) to a Fraction**:
- To add \( \frac{3}{7} \) and \( 0.89 \), we can convert \( 0.89 \) into a fraction.
- \( 0.89 = \frac{89}{100} \).

4. **Find a Common Denominator**:
- The least common multiple of \( 7 \) and \( 100 \) is \( 700 \).
- Convert both fractions:
\[ \frac{3}{7} = \frac{3 \times 100}{7 \times 100} = \frac{300}{700} \]
\[ 0.89 = \frac{89 \times 7}{100 \times 7} = \frac{623}{700} \]

5. **Add the Two Fractions**:
- Now we can add the two fractions:
\[ \frac{300}{700} + \frac{623}{700} = \frac{300 + 623}{700} = \frac{923}{700} \]

6. **Write the Final Exponent**:
- Therefore, we can write:
\[ 95^{\frac{3}{7}} \times 95^{0.89} = 95^{\frac{923}{700}} \]

7. **Conclusion**:
- Thus, the value of \( ? \) is \( \frac{923}{700} \).

### Final Answer:
\[ ? = \frac{923}{700} \]