Question

select the equivalent expression.$left(x^{-3} cdot y^{3}
ight)^{-7} =?$choose 1 answer:a $x^{-10} cdot y^{-4}$b $(xy)^{0}$c $x^{21} cdot y^{-21}$

Explanation:

Step1: Apply power of a product rule

$$(x^{-3} \cdot y^{3})^{-7} = (x^{-3})^{-7} \cdot (y^{3})^{-7}$$

Step2: Apply power of a power rule

$$(x^{-3})^{-7} = x^{(-3) \times (-7)} = x^{21}, \quad (y^{3})^{-7} = y^{3 \times (-7)} = y^{-21}$$

Step3: Combine the results

$$x^{21} \cdot y^{-21}$$

Answer:

C. $x^{21} \cdot y^{-21}$