`9^(2)xx(1)/(6561)xx729=9^(?)`

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To solve the equation \( 9^2 \times \frac{1}{6561} \times 729 = 9^? \), we will simplify the left side step by step.

### Step 1: Rewrite the numbers as powers of 9
First, we need to express \( 6561 \) and \( 729 \) as powers of \( 9 \).

- We know that \( 9 = 3^2 \), so:
\[ 9^2 = (3^2)^2 = 3^4 \]

- Now, let's find \( 6561 \):
\[ 6561 = 9^4 \quad \text{(since \( 9^4 = (3^2)^4 = 3^8 \))} \]

- Next, we find \( 729 \):
\[ 729 = 9^3 \quad \text{(since \( 9^3 = (3^2)^3 = 3^6 \))} \]

### Step 2: Substitute the powers into the equation
Now, we can rewrite the equation using these powers:
\[ 9^2 \times \frac{1}{9^4} \times 9^3 \]

### Step 3: Simplify the expression
Using the properties of exponents, we can simplify the left side:
\[ 9^2 \times 9^{-4} \times 9^3 = 9^{2 - 4 + 3} \]

### Step 4: Calculate the exponent
Now, we calculate the exponent:
\[ 2 - 4 + 3 = 1 \]
Thus, we have:
\[ 9^{2 - 4 + 3} = 9^1 \]

### Step 5: Write the final equation
Now we can equate both sides:
\[ 9^1 = 9^? \]
This implies:
\[ ? = 1 \]

### Final Answer
The value of \( ? \) is \( 1 \).

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