Math question! raising exponents to powers! please help!

So I need to find x. The eqatuon is (5^x^2) * (5^7x) = 25^-5
the first one^ is FIVE raised to the X raised to the 2. like the x is squared. I don't know how to do that! please help!

remember these rules:

a^b = a^c, then b = c

and

a^b * a^c = a^(b + c)


5^(x^2) * 5^(7x) = 25^(-5)

25 = 5^2, so 25^(-5) = 5^(2 * (-5)) = 5^(-10)

5^(x^2) * 5^(7x) = 5^(-10)
5^(x^2 + 7x) = 5^(-10)
x^2 + 7x = -10
x^2 + 7x + 10 = 0
(x + 5) * (x + 2) = 0
x = -2 , -5

well, when you multiply two numbers with the same base, you can add their exponents, so:

5^( (x^2)+7x ) = 5 ^ 2 (^-5)
and you can multiply the 2 with the -5 = -10

so then the bases are equal on both sides, and you can just set the exponents equal to each other:
x^2 + 7x = -10
x^2 + 7x + 10 = 0

x = -5, x = -2