Answer :
To simplify the expression \(\left(\frac{x}{x^2 y^2}\right)\), follow these steps:
1. Identify the variables in the numerator and the denominator:
- The numerator is \(x\).
- The denominator is \(x^2 y^2\).
2. Rewrite the expression to separate terms involving \(x\) and \(y\):
[tex]\[ \frac{x}{x^2 y^2} \][/tex]
can be rewritten as:
[tex]\[ \frac{x}{x^2} \cdot \frac{1}{y^2} \][/tex]
3. Simplify the term \(\frac{x}{x^2}\):
\(x^2\) can be expressed as \(x \cdot x\). Therefore, we can simplify:
[tex]\[ \frac{x}{x \cdot x} = \frac{1}{x} \][/tex]
4. Combine the simplified results:
Now, we combine the simplified terms:
[tex]\[ \frac{1}{x} \cdot \frac{1}{y^2} = \frac{1}{x \cdot y^2} \][/tex]
Thus, the simplified form of the expression \(\left(\frac{x}{x^2 y^2}\right)\) is:
[tex]\[ \frac{1}{x \cdot y^2} \][/tex]
Therefore, the final answer is:
[tex]\[ \boxed{\frac{1}{x y^2}} \][/tex]
1. Identify the variables in the numerator and the denominator:
- The numerator is \(x\).
- The denominator is \(x^2 y^2\).
2. Rewrite the expression to separate terms involving \(x\) and \(y\):
[tex]\[ \frac{x}{x^2 y^2} \][/tex]
can be rewritten as:
[tex]\[ \frac{x}{x^2} \cdot \frac{1}{y^2} \][/tex]
3. Simplify the term \(\frac{x}{x^2}\):
\(x^2\) can be expressed as \(x \cdot x\). Therefore, we can simplify:
[tex]\[ \frac{x}{x \cdot x} = \frac{1}{x} \][/tex]
4. Combine the simplified results:
Now, we combine the simplified terms:
[tex]\[ \frac{1}{x} \cdot \frac{1}{y^2} = \frac{1}{x \cdot y^2} \][/tex]
Thus, the simplified form of the expression \(\left(\frac{x}{x^2 y^2}\right)\) is:
[tex]\[ \frac{1}{x \cdot y^2} \][/tex]
Therefore, the final answer is:
[tex]\[ \boxed{\frac{1}{x y^2}} \][/tex]
