`17^(3.5)xx17^(7.3)/17^(4.2)=17^(?)`

Options

A. 8.4
B. 8
C. 6.6
D. 6.4

Answer

To solve the expression \( \frac{17^{3.5} \times 17^{7.3}}{17^{4.2}} = 17^{?} \), we can follow these steps:

### Step 1: Combine the powers in the numerator
Using the property of exponents that states \( a^m \times a^n = a^{m+n} \), we can combine the powers in the numerator:

\[ 17^{3.5} \times 17^{7.3} = 17^{3.5 + 7.3} \]

### Step 2: Calculate the sum of the powers
Now, we add the exponents:

\[ 3.5 + 7.3 = 10.8 \]

So, we can rewrite the expression as:

\[ \frac{17^{10.8}}{17^{4.2}} \]

### Step 3: Apply the division property of exponents
Using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify the expression:

\[ \frac{17^{10.8}}{17^{4.2}} = 17^{10.8 - 4.2} \]

### Step 4: Calculate the difference of the powers
Now, we subtract the exponents:

\[ 10.8 - 4.2 = 6.6 \]

### Step 5: Write the final answer
Thus, we have:

\[ 17^{10.8 - 4.2} = 17^{6.6} \]

So, the final answer is:

\[ 17^{?} = 17^{6.6} \]

### Summary of the solution:
The overall expression simplifies to \( 17^{6.6} \).

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