<u>Given</u><u> info</u><u>:</u><u>-</u><u> </u>What number should [(-5/3)³]^-3 be multiply obtain (-3/5)⁴ ?
<u>Explanation</u><u>:</u><u>-</u>
Given number = [(-5/3)³]^-3
Let the required number be X
On multiplying [(-5/3)³]^-3 with X
⇛ [(-5/3)³]^-3 × X
According to the given problem
The result = (-3/5)⁴
⇛ [(-5/3)³]^-3 × X = (-3/5)⁴
⇛ (-5/3)^(3×-3) × X = (-3/5)⁴
Since (a^m)^n = a^mn
⇛ (-5/3)^-9 ×X = (-3/5)⁴
⇛(-3/5)⁹ ×X = (-3/5)⁴
Since a^-n = 1/a^n
⇛X = (-3/5)⁴/(-3/5)⁹
⇛X = (-3/5)^(4-9)
Since a^m / a^n = a^(m-n)
⇛ X = (-3/5)^-5
⇛ X = (-5/3)⁵
Since a^-n = 1/a^n
Therefore, X = (-5/3)⁵
<u>The required number for the given problem is (-5/3)</u><u>⁵</u><u>.</u>
24 students ===> 100% of the third test &
150% of the second test is 150% of 24 students:
So the 150% in the second test correspond to 150% x 24 = 36
