expand x^(4-2x)

To expand the expression \(x^{(4-2x)}\), we can use the properties of exponents. The exponent, \(4-2x\), indicates that we have to raise \(x\) to the power of \(4-2x\).

Let's break it down step by step:

Step 1: Distribute the exponent to each term inside the parentheses.
\(x^{4-2x} = x^4 \cdot x^{-2x}\)

Step 2: Simplify the expression \(x^{-2x}\).
The negative exponent \(x^{-2x}\) can be rewritten as \(\frac{1}{x^{2x}}\).

Step 3: Combine the terms.
\(x^{4-2x} = x^4 \cdot \frac{1}{x^{2x}}\)

Step 4: Simplify by applying the rule of exponents.
When dividing two exponential terms with the same base, you subtract the exponents.
\(x^{4-2x} = \frac{x^4}{x^{2x}} = x^{4-2x} = \frac{x^4}{x^{2x}} = x^{4-(2x)} = x^{4-2x}\)

So, the expanded form of the expression \(x^{4-2x}\) is \(x^4 \cdot \frac{1}{x^{2x}}\), or equivalently, \( \frac{x^4}{x^{2x}} \).