Final answer:
The expression 1/√x² × 1/2√x² simplifies to 1/x × 1/(2x), which results in 1/(2x²). So, the correct simplified form is 1/x². Therefore, the simplified expression is 1/(2x²), which corresponds to option c.
Step-by-step explanation:
To simplify the expression 1/√x² × 1/2√x², we should first understand the properties of exponents and radicals. We know that x² is equivalent to √x because √x multiplied by itself gives x. If we factor the given expression, it simplifies as:
1/√x² × 1/2√x² = 1/x × 1/(2x)
If we multiply these fractions, the exponents on x add up because when multiplied, bases with the same exponents should be added together according to the properties of exponents and radicals. Thus, we get:
(1×1)/(x×2x) = 1/(2x²)To simplify the given expression, we can start by multiplying the two fractions together:
1/√x² × 1/2√x² = 1/(√x² × 2√x²)
Next, we can simplify the expression inside the parentheses by multiplying the square roots:
1/(√x² × 2√x²) = 1/(x × 2x) = 1/(2x²)
Therefore, the simplified expression is 1/(2x²), which corresponds to option c.