Exponent Rules and Rational Exponents Explained

The video tutorial reviews rational exponents, explaining how exponents that look like fractions can be interpreted. It demonstrates how to rewrite expressions with rational exponents, using examples to show the relationship between the numerator and denominator of the exponent. The tutorial includes a practice problem to reinforce the concept of converting expressions into fractional exponent form.

What is an example of a rational exponent?

• The square root of 2

• 2 to the power of 3/4

• 2 to the power of 4

• 3/4

How can you rewrite 2 to the power of 3/4?

• The cube root of 2 to the fourth

• The fourth root of 2 cubed

• 2 to the power of 4/3

• The square root of 2

What does the bottom part of a rational exponent represent?

• The base of the exponent

• The type of root

• The power to which the base is raised

• The numerator of the fraction

What does the top part of a rational exponent indicate?

• The denominator of the fraction

• The power to which the base is raised

• The base of the exponent

• The type of root

In the expression 2 to the power of 3/4, what does 4 represent?

• The base of the exponent

• The power to which the base is raised

• The type of root

• The numerator of the fraction

How is the quarter root of x to the power 5 written in rational exponent form?

• x to the power of 5/4

• x to the power of 4/5

• The fifth root of x to the fourth

• x squared

What is the base in the expression 'the quarter root of x to the power 5'?

• 5

• 1/4

• x

• 4

In the expression 'the quarter root of x to the power 5', what does 5 represent?

• The base of the exponent

• The type of root

• The power to which the base is raised

• The denominator of the fraction

Convert 3 to the power of 3/7 into its equivalent root form.

• 3 to the power of 7/3

• The third root of 3 to the seventh

• The cube root of 3 to the seventh

• The seventh root of 3 cubed