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

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))
Solve for y.
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
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)

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