10^(3x-10)=(1/100)^(6x-1) Solve the equation.

To evaluate the given equation 10^(3x-10)=(1/100)^(6x-1) , we may apply 100=10^2 . The equation becomes:
10^(3x-10)=(1/10^2)^(6x-1)
Apply Law of Exponents: 1/x^n = x^(-n) .
10^(3x-10)=(10^(-2))^(6x-1)
Note: 1/100= 10^(-2)
Apply Law of Exponents: (x^n)^m = x^(n*m) .
10^(3x-10)=10^((-2)*(6x-1))
10^(3x-10)=10^(-12x+2)
Apply the theorem: If b^x=b^y then x=y , we get:
3x-10=-12x+2
Add 12x on both sides of the equation.
3x-10+12x=-12x+2+12x
15x-10=2
Add 10 on both sides of the equation.
15x-10+10=2+10
15x=12
Divide both sides by 15 .
(15x)/15=12/15
x=12/15
Simplify.
x=4/5
Checking: Plug-in x=4/5 on 10^(3x-10)=(1/100)^(6x-1) .
10^(3*(4/5)-10)=?(1/100)^(6*(4/5)-1)
10^(12/5-10)=?(1/100)^(24/5-1)
10^(12/5-50/5)=?(1/100)^(24/5-5/5)
10^((-38)/5)=?(1/100)^(19/5)
10^((-38)/5)=?(10^(-2))^(19/5)
10^((-38)/5)=?10^((-2)*19/5)
10^((-38)/5)=10^((-38)/5)   TRUE
Thus, the x=4/5  is the real exact solution of the equation 10^(3x-10)=(1/100)^(6x-1) .