# Algebra Examples

Write as an equation.

Interchange the variables.

Rewrite the equation as .

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

Simplify .

Combine the numerators over the common denominator.

Rewrite as .

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

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.

Simplify the numerator.

Rewrite as .

Raise to the power of .

Simplify with factoring out.

Combine using the product rule for radicals.

Reorder factors in .

Replace the with to show the final answer.

To verify the inverse, check if and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify the numerator.

Subtract from .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming real numbers.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify each term.

Apply the product rule to .

Simplify the numerator.

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 .

Simplify.

Apply the distributive property.

Multiply by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Raise to the power of .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Combine the opposite terms in .

Add and .

Add and .

Since and , then is the inverse of .