Simplify the expression. $$ \left(\frac{2}{x y}\right)^{6} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \left(\frac{2}{x y}\right)^{6} $$, follow these steps:

1. **Apply the exponent to both the numerator and the denominator**:
   $$
   \left(\frac{2}{x y}\right)^6 = \frac{2^6}{(x y)^6}
   $$

2. **Calculate $$ 2^6 $$**:
   $$
   2^6 = 64
   $$

3. **Expand $$ (x y)^6 $$ using the property $$(ab)^n = a^n b^n$$**:
   $$
   (x y)^6 = x^6 y^6
   $$

4. **Combine the results**:
   $$
   \frac{64}{x^6 y^6}
   $$

**Final Simplified Form**:
$$
\frac{64}{x^{6} y^{6}}
$$
The simplified form of the expression is $$ \frac{64}{x^{6} y^{6}} $$.

Simplify the expression. \( \left(\frac{2}{x y}\right)^{6} \)