If `2^(4)times4^(2)=16^(x)`, then x=

Answer

To solve the equation \(2^4 \times 4^2 = 16^x\), we will express all terms in terms of base 2.

### Step 1: Rewrite the equation
We start with:
\[ 2^4 \times 4^2 = 16^x \]

### Step 2: Express \(4\) and \(16\) in terms of \(2\)
We know that:
\[ 4 = 2^2 \quad \text{and} \quad 16 = 2^4 \]
Now, substituting these values into the equation gives:
\[ 2^4 \times (2^2)^2 = (2^4)^x \]

### Step 3: Simplify the left side
Using the power of a power property \((a^m)^n = a^{m \cdot n}\), we can simplify \( (2^2)^2 \):
\[ (2^2)^2 = 2^{2 \cdot 2} = 2^4 \]
So, the left side becomes:
\[ 2^4 \times 2^4 \]

### Step 4: Combine the powers on the left side
Using the property of exponents \(a^m \times a^n = a^{m+n}\):
\[ 2^4 \times 2^4 = 2^{4+4} = 2^8 \]

### Step 5: Simplify the right side
Now we simplify the right side:
\[ (2^4)^x = 2^{4x} \]

### Step 6: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal to each other:
\[ 8 = 4x \]

### Step 7: Solve for \(x\)
To find \(x\), divide both sides by 4:
\[ x = \frac{8}{4} = 2 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{2} \]