(2a⁻²y⁻³)¹/₂
Solution:
[tex]2 ^{ \frac{1}{2} } a ^{ \frac{-2}{2} } y ^{ \frac{-3}{2} } [/tex]
[tex] \sqrt{2} /ay ^{ \frac{3}{2} } [/tex]
As rational exponent:
[tex]2 ^{1/2} / ay^{3/2} [/tex]
Simplified (rationalize the denominator):
[tex] \frac{ \sqrt{2} }{ay \sqrt{y} } * \frac{ay \sqrt{y} }{ay \sqrt{y} } [/tex]
[tex] \frac{ay \sqrt{2y} }{a ^{2} y ^{3} } [/tex]
Final answer: [tex] \frac{ \sqrt{2y} }{ay^{2} } [/tex]
