(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)

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

Add -36 and 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)