If x=(−25)30÷(5−2)−28 and y=(−25)2×(−25)3, then find the value of (x3÷y)2.
Given, x=(−25)30÷(5−2)−28 and y=(−25)2×(−25)3
x=(−25)30÷(5−2)−28
=(−25)30÷(−25)28[∵(a)−m=1am]
= (−25)30−28 [∵aman = am−n]
= (−25)2
⟹x3= [(−25)2]3
i.e., x3=(−25)6 ⋯(i)
[∵(am)n = amn]
y=(−25)2×(−25)3
⟹y=(−25)2+3 [∵am×an = am+n]
i.e., y=(−25)5 ⋯(ii)
∴From (i) and (ii),x3÷y=(−25)6(−25)5
=(−25)6−5 [∵aman = am−n]
=−25
∴(x3÷y)2=425