Simplify (6/xy)²: Converting Squared Fraction Expression

Insert the corresponding expression:

$\left(\frac{6}{x\times y}\right)^2=$

To solve this problem, we'll apply the rule for powers of a fraction:

• Step 1: Identify the fraction. The fraction given is $\frac{6}{x \times y}$.
• Step 2: Apply the power to both the numerator and the denominator. This means squaring both 6 and $x \times y$.
• Step 3: Calculate the square of the numerator and the denominator:
• The square of the numerator: $6^2 = 36$.
• The square of the denominator: $(x \times y)^2 = x^2 \times y^2$.
• Step 4: Combine the results: $\left(\frac{6}{x \times y}\right)^2 = \frac{6^2}{(x \times y)^2} = \frac{36}{x^2 \times y^2}$.

Thus, the expression $\left(\frac{6}{x \times y}\right)^2$ simplifies to $\frac{36}{(x \times y)^2}$.

Therefore, the correct answer is clearly the expression $\frac{36}{(x \times y)^2}$, which matches choice 4.