What should come in place of the question mark (?) in the following questions:
`3^15 xx 9^22` `div` 27 = `(3)^?`

Options

A. 37
B. 46
C. 56
D. 49

Answer

To solve the equation \( \frac{3^{15} \times 9^{22}}{27} = 3^{?} \), we will first express all the terms in the equation using the base 3.

### Step 1: Rewrite \( 9^{22} \) and \( 27 \) in terms of base 3.
- We know that \( 9 = 3^2 \), so:
\[ 9^{22} = (3^2)^{22} = 3^{2 \times 22} = 3^{44} \]
- We also know that \( 27 = 3^3 \).

### Step 2: Substitute these values back into the equation.
Now we can rewrite the equation as:
\[ \frac{3^{15} \times 3^{44}}{3^3} = 3^{?} \]

### Step 3: Combine the powers of 3 in the numerator.
Using the property of exponents that states \( a^m \times a^n = a^{m+n} \):
\[ 3^{15 + 44} = 3^{59} \]
So now our equation looks like:
\[ \frac{3^{59}}{3^3} = 3^{?} \]

### Step 4: Simplify the left side using the property of exponents.
Using the property \( \frac{a^m}{a^n} = a^{m-n} \):
\[ 3^{59 - 3} = 3^{?} \]
This simplifies to:
\[ 3^{56} = 3^{?} \]

### Step 5: Set the exponents equal to each other.
Since the bases are the same, we can equate the exponents:
\[ ? = 56 \]

Thus, the value that should come in place of the question mark is:
\[ \boxed{56} \]