Answer:
Answer is a^8/b^10
Option C
Explanation:
((a²b-³)/(a-²b²))² where b and a are not equal zero
To solve this equation we start solving the equation from inside the bracket. And for simplicity we solve the numerator and solve the denominator before dividing them with each other. Now let get started
((a²b-³)/(a-²b²))²
Recall from indices that
a ^ -b = 1/a^b
I.e b-³ = 1/b³... We will apply this here.
((a²b-³)/(a-²b²))²
=((a²* 1/b³)/(b²*1/a²))²
=((a²/b³)/(b²/a²))²
Also recall that
(a/b) / (c/d) = (a/b) * (d/c)
Therefore
=((a²/b³)/(b²/a²))²
=(a²/b³ * a²/b²)²
Recall that: a^b * a^c = a^(b+c)
= (a ^ (2+2) / b ^ (2+3))²
= (a^4/b^5)²
Recall that: (a^b)^c = a^(b+c)
Therefore:
=™(a^4/b^5)²
=(a^(4*2)/b^(5*2))
= a^8/b^10