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 .

Add and .

Expand by multiplying each term in the first expression by each term in the second expression.

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

Combine the numerators over the common denominator.

Add and .

Divide by .

Simplify .

Apply the distributive property.

Multiply by .

Move to the left of .

Multiply by .

Multiply by .

Simplify by adding terms.

Combine the opposite terms in .

Subtract from .

Add and .

Subtract from .

Subtract from .

Reorder factors in .

Graph each side of the equation. The solution is the x-value of the point of intersection.

Solve by Factoring (x-4)^(3/2)=27