53-y=(125)2y+4

Apply the product rule to 125.

53-y=12y+4252y+4

One to any power is one.

53-y=1252y+4

Move 252y+4 to the numerator using the negative exponent rule 1b-n=bn.

53-y=25-(2y+4)

Create equivalent expressions in the equation that all have equal bases.

53-y=52(-(2y+4))

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

3-y=2(-(2y+4))

Simplify 2(-(2y+4)).

Apply the distributive property.

3-y=2(-(2y)-1⋅4)

Multiply.

Multiply 2 by -1.

3-y=2(-2y-1⋅4)

Multiply -1 by 4.

3-y=2(-2y-4)

3-y=2(-2y-4)

Apply the distributive property.

3-y=2(-2y)+2⋅-4

Multiply.

Multiply -2 by 2.

3-y=-4y+2⋅-4

Multiply 2 by -4.

3-y=-4y-8

3-y=-4y-8

3-y=-4y-8

Move all terms containing y to the left side of the equation.

Add 4y to both sides of the equation.

3-y+4y=-8

Add -y and 4y.

3+3y=-8

3+3y=-8

Move all terms not containing y to the right side of the equation.

Subtract 3 from both sides of the equation.

3y=-8-3

Subtract 3 from -8.

3y=-11

3y=-11

Divide each term by 3 and simplify.

Divide each term in 3y=-11 by 3.

3y3=-113

Cancel the common factor of 3.

Cancel the common factor.

3y3=-113

Divide y by 1.

y=-113

y=-113

Move the negative in front of the fraction.

y=-113

y=-113

y=-113

The result can be shown in multiple forms.

Exact Form:

y=-113

Decimal Form:

y=-3.6‾

Mixed Number Form:

y=-323

Solve for y 5^(3-y)=(1/25)^(2y+4)