Rational Exponents and Roots

The video tutorial explains rational exponents, which are fractional exponents, and how to handle them, including negative exponents. It covers two methods for solving rational exponents: taking the power first or the root first. Examples are provided to illustrate these methods, such as solving 8 to the 2/3 and 27 to the negative 2/3. The tutorial also demonstrates how to use rational exponents in equations by raising both sides to the reciprocal power.

What does the numerator in a rational exponent represent?

• The power to which the base is raised

• The negative of the base

• The root of the expression

• The reciprocal of the base

How does a negative exponent affect an expression?

• It squares the expression

• It takes the reciprocal of the expression

• It doubles the expression

• It halves the expression

What is the first step in solving 8 to the 2/3 power using the root-first method?

• Multiply 8 by 2

• Take the cube root of 8

• Divide 8 by 3

• Square the number 8

In the expression 27 to the negative 2/3, what does the negative sign indicate?

• To add 27 to the power

• To multiply the expression by 2

• To subtract 27 from the power

• To take the reciprocal of the expression

What is the result of 27 to the negative 2/3 after taking the reciprocal and solving?

• 9

• 1/9

• 27

• 3

What is the cube root of 8?

• 3

• 4

• 2

• 1

What is the result of 2 squared?

• 5

• 4

• 3

• 2

What is the cube root of 27?

• 5

• 4

• 3

• 2

What is the result of 3 squared?

• 9

• 7

• 6

• 8

When solving equations with rational exponents, what is a common strategy?

• Add the exponents

• Subtract the exponents

• Raise both sides to the reciprocal power

• Divide both sides by the exponent