Help: exponential function equations step by step

Hard to read the frst one but I assume this is :

1. 5^{16 -(x^2 - x)}  =  25^{-(x^2 - 8)}   simplify as

   5 ^{-x^2 + x + 16}  =  (5²) ^{8 - x^2} 

    5 ^{-x^2 + x + 16}  =  5^{16 -x^2}      

Since the bases are the same.....solve for the exponents

-x^2 + x + 16   =   16  - x^2    subtract x^2 from both sides

x + 16  =  16       subtract 16 from both sides

x  = 0

Here's the second one

25^4x  = (1/5)^{x^2}

Note that 1/5  =  5^-1    and 25  = 5^2 ....so we have....

(5^2)^4x =  (5^-1)^{x^2}

5^8x =  5^{-x^2}    the bases are the same....solve for the exponents

8x  = -x^2     add x^2 to both sides

x^2 + 8x  = 0      factor

x ( x + 8)  = 0       set both factors to 0  and solve for x and we get that

x = 0    or   x  = -8