If x and y are non-negative, simplify (81 x17 y18 )\(\frac{1}{4}\)

If x and y are non-negative, simplify (81 x¹⁷ y¹⁸ )^{\(\frac{1}{4}\)}

A 81 x^{\(\frac{{17}}{4}\)} y^{\(\frac{9}{2}\)}

B 9 x^{\(\frac{{17}}{4}\)} y^{\(\frac{7}{2}\)}

C 3 x^{\(\frac{{15}}{4}\)} y^{\(\frac{9}{2}\)}

D 3 x^{\(\frac{{17}}{4}\)} y^{\(\frac{9}{2}\)}

Correct Answer: Option D

Solution:

যদি x এবং y ঋণাত্মক না হয়, তবে (81 x¹⁷ y¹⁸ )^{\(\frac{1}{4}\)}

এর মানে সরলীকরণ করতে হবে ।

প্রদত্ত রাশি = (81 x¹⁷ y¹⁸ )^{\(\frac{1}{4}\)} = ( 3⁴ \( \times \) x¹⁷ \( \times \) y¹⁸ )^{\(\frac{1}{4}\)}

= ( 3^{\(\frac{4}{4}\)} \( \times \) x^{\(\frac{{17}}{4}\)} \( \times \) y^{\(\frac{{18}}{4}\)} ) = 3 x^{\(\frac{{17}}{4}\)} y^{\(\frac{9}{2}\)}