Solve by Factoring x^-3=1/64

Math
Move to the left side of the equation by subtracting it from both sides.
Rewrite the expression using the negative exponent rule .
Rewrite as .
Rewrite as .
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Apply the product rule to .
One to any power is one.
Multiply and .
Move to the left of .
Multiply by .
Apply the product rule to .
One to any power is one.
Raise to the power of .
Reorder terms.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Reorder terms.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Reorder terms.
Rewrite in a factored form.
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Apply the distributive property.
Multiply by .
Factor each term.
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Multiply and .
Multiply by .
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Find the LCD of the terms in the equation.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The prime factors for are .
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has factors of and .
has factors of and .
has factors of and .
has factors of and .
has factors of and .
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The LCM of is .
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
The factors for are , which is multiplied by each other times.
occurs times.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Simplify .
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Multiply by .
Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
The LCM for is the numeric part multiplied by the variable part.
Multiply each term by and simplify.
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Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
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Reduce the expression by cancelling the common factors.
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Rewrite using the commutative property of multiplication.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
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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Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Combine the opposite terms in .
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Add and .
Add and .
Add and .
Add and .
Multiply .
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Multiply by .
Multiply by .
Solve the equation.
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Subtract from both sides of the equation.
Move to the left side of the equation by adding it to both sides.
Factor the left side of the equation.
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Factor out of .
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Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Factor.
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Simplify.
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Move to the left of .
Raise to the power of .
Remove unnecessary parentheses.
Multiply each term in by
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Multiply each term in by .
Simplify .
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Simplify by multiplying through.
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Apply the distributive property.
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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Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify terms.
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Combine the opposite terms in .
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Add and .
Add and .
Add and .
Add and .
Apply the distributive property.
Multiply .
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Add to both sides of the equation.
Move to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
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Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Move to the left of .
Raise to the power of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
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Set the next factor equal to .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Simplify .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Simplify .
Change the to .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Simplify .
Change the to .
The final answer is the combination of both solutions.
The final solution is all the values that make true.
Solve by Factoring x^-3=1/64
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