Understanding and Solving Equations

The video tutorial explains how to solve a given equation by rewriting x to the one-half as the square of x to the one-fourth using the power to power property. It then guides through subtracting x to the one-fourth from both sides and factoring the equation. The tutorial continues by solving the factored equation, leading to two solutions: x equals zero and x equals one.

What is the initial step in solving the given equation?

• Add one to both sides

• Factor out x to the power of one-fourth

• Rewrite x to the one-half as the square of x to the one-fourth

• Subtract x to the one-fourth from both sides

Which property is used to rewrite x to the one-half as the square of x to the one-fourth?

• Commutative property

• Power to power property

• Distributive property

• Associative property

What is the next step after rewriting the equation in the given problem?

• Add x to the one-fourth to both sides

• Subtract x to the one-fourth from both sides

• Multiply both sides by x to the one-fourth

• Divide both sides by x to the one-fourth

How is the left side of the equation factored?

• By factoring out x to the power of one-fourth

• By factoring out x to the power of one

• By factoring out x to the power of zero

• By factoring out x to the power of one-half

What is the solution to the equation x to the power of one-fourth equals zero?

• x equals negative one

• x equals two

• x equals one

• x equals zero

What is the solution to the equation x to the power of one-fourth minus one equals zero?

• x equals zero

• x equals one

• x equals two

• x equals negative one