Solve for v (1/64)^(3v-2)=16^(2v+1)

Math
(164)3v-2=162v+1
Apply the product rule to 164.
13v-2643v-2=162v+1
One to any power is one.
1643v-2=162v+1
Move 643v-2 to the numerator using the negative exponent rule 1b-n=bn.
64-(3v-2)=162v+1
Create equivalent expressions in the equation that all have equal bases.
43(-(3v-2))=42(2v+1)
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
3(-(3v-2))=2(2v+1)
Solve for v.
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Simplify 3(-(3v-2)).
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Apply the distributive property.
3(-(3v)–2)=2(2v+1)
Multiply.
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Multiply 3 by -1.
3(-3v–2)=2(2v+1)
Multiply -1 by -2.
3(-3v+2)=2(2v+1)
3(-3v+2)=2(2v+1)
Apply the distributive property.
3(-3v)+3⋅2=2(2v+1)
Multiply.
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Multiply -3 by 3.
-9v+3⋅2=2(2v+1)
Multiply 3 by 2.
-9v+6=2(2v+1)
-9v+6=2(2v+1)
-9v+6=2(2v+1)
Simplify 2(2v+1).
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Apply the distributive property.
-9v+6=2(2v)+2⋅1
Multiply.
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Multiply 2 by 2.
-9v+6=4v+2⋅1
Multiply 2 by 1.
-9v+6=4v+2
-9v+6=4v+2
-9v+6=4v+2
Move all terms containing v to the left side of the equation.
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Subtract 4v from both sides of the equation.
-9v+6-4v=2
Subtract 4v from -9v.
-13v+6=2
-13v+6=2
Move all terms not containing v to the right side of the equation.
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Subtract 6 from both sides of the equation.
-13v=2-6
Subtract 6 from 2.
-13v=-4
-13v=-4
Divide each term by -13 and simplify.
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Divide each term in -13v=-4 by -13.
-13v-13=-4-13
Cancel the common factor of -13.
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Cancel the common factor.
-13v-13=-4-13
Divide v by 1.
v=-4-13
v=-4-13
Dividing two negative values results in a positive value.
v=413
v=413
v=413
The result can be shown in multiple forms.
Exact Form:
v=413
Decimal Form:
v=0.307692‾
Solve for v (1/64)^(3v-2)=16^(2v+1)

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