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 .

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify.

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 .

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.

Raise to the power of .

Set the next factor equal to .

Find a common factor that is present in each term.

Substitute for .

Solve for .

Multiply by .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

Change the to .

Rewrite as .

Factor out of .

Factor out of .

Move the negative in front of the fraction.

Simplify the expression to solve for the portion of the .

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

Change the to .

Rewrite as .

Factor out of .

Factor out of .

Move the negative in front of the fraction.

The final answer is the combination of both solutions.

Substitute for .

Solve for for .

Raise each side of the equation to the power to eliminate the fractional exponent on the left side.

Simplify .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Simplify the expression.

Raise to the power of .

Multiply by .

Raise to the power of .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Multiply by .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Multiply by .

Subtract from .

Subtract from .

Reorder and .

Cancel the common factor of and .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Factor out of .

Factor out of .

Move the negative in front of the fraction.

Solve for for .

Raise each side of the equation to the power to eliminate the fractional exponent on the left side.

Simplify .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Simplify the expression.

Raise to the power of .

Multiply by .

Raise to the power of .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Multiply by .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Multiply by .

Subtract from .

Add and .

Reorder and .

Cancel the common factor of and .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Factor out of .

Factor out of .

Move the negative in front of the fraction.

List all of the solutions.

The final solution is all the values that make true.

Solve by Factoring x^(3/2)=27