# Evaluate 5^(x^2)*5^(-4x)=3125 5×2⋅5-4x=3125
Use the power rule aman=am+n to combine exponents.
5×2-4x=3125
Create equivalent expressions in the equation that all have equal bases.
5×2-4x=55
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
x2-4x=5
Solve for x.
Move 5 to the left side of the equation by subtracting it from both sides.
x2-4x-5=0
Factor x2-4x-5 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -5 and whose sum is -4.
-5,1
Write the factored form using these integers.
(x-5)(x+1)=0
(x-5)(x+1)=0
Set x-5 equal to 0 and solve for x.
Set the factor equal to 0.
x-5=0
Add 5 to both sides of the equation.
x=5
x=5
Set x+1 equal to 0 and solve for x.
Set the factor equal to 0.
x+1=0
Subtract 1 from both sides of the equation.
x=-1
x=-1
The solution is the result of x-5=0 and x+1=0.
x=5,-1
x=5,-1
Evaluate 5^(x^2)*5^(-4x)=3125

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