Answer:
10/3
Step-by-step explanation:
( 5/2 )^-15 can also be written as ( 2/5 )^15.
So,
( 2/5 )^-3 x ( 2/5 )^15 = ( 2/5 )^( 2 + 3y )
Formulas : -
1. a^m x a^n = a^c
2. a^m x a^n = a^( m + n )
3. a^( m + n ) = a^c
Here ( m + n ) and c are powers.
a is the base.
Since bases are same on both sides, their powers are also same,
so m + n = c.
Here,
a = 2/5
m = - 3
n = 15
c = 2 + 3y
Substitute the values of m, n & c in " m + n = c ",
m + n = c
- 3 + 15 = 2 + 3y
15 - 3 = 2 + 3y
12 = 2 + 3y
12 - 2 = 3y
10 = 3y
y = 10/3