Value of ? In expression
`7^(8.9)/(343)^(1.7)xx(49)^(4.8)=7^(?)` is

Options

A. a. 13.4
B. b. 12.8
C. c. 11.4
D. d. 9.6

Answer

To solve the expression \( \frac{7^{8.9}}{(343)^{1.7} \times (49)^{4.8}} = 7^{?} \), we will first express the bases \( 343 \) and \( 49 \) in terms of base \( 7 \).

### Step 1: Rewrite the bases
- We know that \( 343 = 7^3 \) and \( 49 = 7^2 \).
- Thus, we can rewrite the expression as:
\[ \frac{7^{8.9}}{(7^3)^{1.7} \times (7^2)^{4.8}} \]

### Step 2: Simplify the expression
- Using the power of a power property, we can simplify:
\[ (7^3)^{1.7} = 7^{3 \times 1.7} = 7^{5.1} \]
\[ (7^2)^{4.8} = 7^{2 \times 4.8} = 7^{9.6} \]
- Now, substituting back into the expression gives us:
\[ \frac{7^{8.9}}{7^{5.1} \times 7^{9.6}} \]

### Step 3: Combine the denominators
- We can combine the powers in the denominator:
\[ 7^{5.1} \times 7^{9.6} = 7^{5.1 + 9.6} = 7^{14.7} \]
- Therefore, the expression now becomes:
\[ \frac{7^{8.9}}{7^{14.7}} = 7^{8.9 - 14.7} \]

### Step 4: Calculate the exponent
- Now we calculate the exponent:
\[ 8.9 - 14.7 = -5.8 \]
- Thus, we have:
\[ 7^{-5.8} \]

### Step 5: Set the expression equal to \( 7^{?} \)
- We can now equate this to \( 7^{?} \):
\[ 7^{-5.8} = 7^{?} \]
- Therefore, we find that:
\[ ? = -5.8 \]

### Final Answer
The value of \( ? \) is \( -5.8 \).