If `x^(2)xx x^(3)xx x = 64` what is x?

Answer

To solve the equation \( x^2 \cdot x^3 \cdot x = 64 \), we will follow these steps:

### Step 1: Combine the Exponents
Using the laws of exponents, we know that when multiplying like bases, we can add the exponents. Therefore, we can rewrite the left side of the equation:

\[ x^2 \cdot x^3 \cdot x = x^{2 + 3 + 1} \]

### Step 2: Simplify the Exponents
Now, we simplify the exponent:

\[ x^{2 + 3 + 1} = x^6 \]

So, we have:

\[ x^6 = 64 \]

### Step 3: Solve for \( x \)
To find \( x \), we need to take the sixth root of both sides of the equation:

\[ x = 64^{\frac{1}{6}} \]

### Step 4: Prime Factorization of 64
Next, we will perform the prime factorization of 64. We can express 64 as:

\[ 64 = 2^6 \]

### Step 5: Substitute Back
Now, substituting back into our equation, we have:

\[ x = (2^6)^{\frac{1}{6}} \]

### Step 6: Simplify the Expression
Using the power of a power property, we simplify:

\[ x = 2^{6 \cdot \frac{1}{6}} = 2^1 \]

### Step 7: Final Answer
Thus, we find:

\[ x = 2 \]

### Summary
The value of \( x \) that satisfies the equation \( x^2 \cdot x^3 \cdot x = 64 \) is:

\[ \boxed{2} \]