Solve by Factoring r^(6/7)=64

Math
Move to the left side of the equation by subtracting it from both sides.
Rewrite as .
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Multiply .
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Combine and .
Multiply by .
Move to the left of .
Raise to the power of .
Reorder terms.
Simplify .
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify terms.
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Combine the opposite terms in .
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Reorder the factors in the terms and .
Add and .
Add and .
Simplify each term.
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Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Add and .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Move .
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Add and .
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Add and .
Move to the left of .
Multiply by .
Multiply by .
Combine the opposite terms in .
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Subtract from .
Add and .
Subtract from .
Add and .
Add to both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Solve the equation for .
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Simplify the right side of the equation.
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Simplify the expression.
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Rewrite as .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Raise to the power of .
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Solve by Factoring r^(6/7)=64


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