Understanding Rational Exponents

What is a rational exponent?

• An exponent that is a whole number

• An exponent that is a fraction

• An exponent that is negative

• An exponent that is zero

What is the first step in solving an equation with a rational exponent?

• Isolate the term with the rational exponent

• Multiply both sides by the reciprocal of the exponent

• Factor the equation

• Add a constant to both sides

When solving a quadratic equation derived from a rational exponent, what should you be cautious of?

• The equation might have only negative solutions

• The equation might have infinite solutions

• The equation might have extraneous solutions

• The equation might have no solutions

How do you eliminate a one-half power in an equation?

• Multiply by 2

• Multiply by 1/2

• Take the square root of both sides

• Square both sides

What is the result of cubing both sides of an equation with a one-third power?

• The exponent becomes one

• The exponent becomes three

• The exponent becomes zero

• The exponent becomes negative

In the context of rational exponents, what does it mean if a solution is extraneous?

• It is a solution that is always negative

• It is a solution that satisfies the original equation

• It is a solution that does not satisfy the original equation

• It is the only solution

What is the cube root of 8 raised to the fourth power?

• 8

• 16

• 32

• 64

What should you do if there are no parentheses around a term with a rational exponent?

• Assume the entire expression is raised to the power

• Only the variable is raised to the power

• Ignore the exponent

• Multiply the entire expression by the exponent

What is the final step in solving an equation with a rational exponent?

• Check for extraneous solutions

• Multiply both sides by the reciprocal of the exponent

• Isolate the term with the rational exponent

• Add a constant to both sides

Why might a graph of a rational exponent equation intersect twice?

• It is a linear graph

• It is a quadratic graph

• It is a graph with a two-thirds power

• It is a cubic graph