# Solve for y (1/25)^(2y+3)=125^(3y-12)

(125)2y+3=1253y-12
Apply the product rule to 125.
12y+3252y+3=1253y-12
One to any power is one.
1252y+3=1253y-12
Move 252y+3 to the numerator using the negative exponent rule 1b-n=bn.
25-(2y+3)=1253y-12
Create equivalent expressions in the equation that all have equal bases.
52(-(2y+3))=53(3y-12)
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2(-(2y+3))=3(3y-12)
Solve for y.
Simplify 2(-(2y+3)).
Apply the distributive property.
2(-(2y)-1⋅3)=3(3y-12)
Multiply.
Multiply 2 by -1.
2(-2y-1⋅3)=3(3y-12)
Multiply -1 by 3.
2(-2y-3)=3(3y-12)
2(-2y-3)=3(3y-12)
Apply the distributive property.
2(-2y)+2⋅-3=3(3y-12)
Multiply.
Multiply -2 by 2.
-4y+2⋅-3=3(3y-12)
Multiply 2 by -3.
-4y-6=3(3y-12)
-4y-6=3(3y-12)
-4y-6=3(3y-12)
Simplify 3(3y-12).
Apply the distributive property.
-4y-6=3(3y)+3⋅-12
Multiply.
Multiply 3 by 3.
-4y-6=9y+3⋅-12
Multiply 3 by -12.
-4y-6=9y-36
-4y-6=9y-36
-4y-6=9y-36
Move all terms containing y to the left side of the equation.
Subtract 9y from both sides of the equation.
-4y-6-9y=-36
Subtract 9y from -4y.
-13y-6=-36
-13y-6=-36
Move all terms not containing y to the right side of the equation.
Add 6 to both sides of the equation.
-13y=-36+6
-13y=-30
-13y=-30
Divide each term by -13 and simplify.
Divide each term in -13y=-30 by -13.
-13y-13=-30-13
Cancel the common factor of -13.
Cancel the common factor.
-13y-13=-30-13
Divide y by 1.
y=-30-13
y=-30-13
Dividing two negative values results in a positive value.
y=3013
y=3013
y=3013
The result can be shown in multiple forms.
Exact Form:
y=3013
Decimal Form:
y=2.307692‾
Mixed Number Form:
y=2413
Solve for y (1/25)^(2y+3)=125^(3y-12)

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