If `(16)^(9) div (16)^(4) xx (16)^(3) = 16^(x)`, then x is equal to

Options

A. 9
B. 8
C. 7
D. 10

Answer

To solve the equation \( (16^9) \div (16^4) \times (16^3) = 16^x \), we will follow the rules of exponents step by step.

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{16^9}{16^4} \times 16^3 \]

### Step 2: Apply the division rule of exponents
According to the rule of exponents, when dividing two powers with the same base, we subtract the exponents:
\[ \frac{16^9}{16^4} = 16^{9-4} = 16^5 \]

### Step 3: Rewrite the expression after division
Now, we can rewrite the expression:
\[ 16^5 \times 16^3 \]

### Step 4: Apply the multiplication rule of exponents
When multiplying two powers with the same base, we add the exponents:
\[ 16^5 \times 16^3 = 16^{5+3} = 16^8 \]

### Step 5: Set the expression equal to \( 16^x \)
Now we have:
\[ 16^8 = 16^x \]

### Step 6: Equate the exponents
Since the bases are the same, we can equate the exponents:
\[ x = 8 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{8} \]