Power Functions and Exponents Concepts

The video tutorial explores power functions with non-integer exponents, starting with fractional exponents and their definitions. It discusses the graphs of power functions for even and odd values of n, highlighting their symmetry properties. The tutorial then defines general power functions and their properties, including how they are defined for different x values. It concludes with a review of calculation rules and encourages students to practice with exercises.

What is the primary restriction when dealing with non-integer exponents?

• They require x to be zero.

• They are only defined for positive x-values.

• They are only applicable to integer values of x.

• They can only be used with negative x-values.

How is x to the power of 1/4 defined?

• As x squared.

• As the fourth root of x.

• As the cube root of x.

• As the square root of x.

For even values of n, the graphs of power functions are defined for:

• Only positive values of x.

• Negative values of x.

• All real values of x.

• Non-negative values of x.

What is x to the power of 2/3 equivalent to?

• The fourth root of x squared.

• The cube root of x squared.

• The square root of x cubed.

• The square of x cubed.

How is x to the power of -5/2 defined?

• 1 over x to the power 5.

• 1 over the fourth root of x to the power 5.

• 1 over the cube root of x to the power 5.

• 1 over the square root of x to the power 5.

What is a key challenge with defining power functions for irrational exponents?

• They are only defined for integer values of x.

• They are always negative.

• They cannot be written as a fraction of two integers.

• They can be easily written as fractions.

For what x values is a power function defined if the exponent 'a' is negative?

• For all x values.

• For x values larger than or equal to zero.

• For x values excluding zero.

• For positive x values only.

What is the behavior of power functions with integer and non-negative exponents?

• Defined only for x equal to zero.

• Defined for all x.

• Defined only for positive x.

• Defined only for negative x.

What is the condition for defining power functions with non-integer exponents for negative x?

• p and q must be even.

• p and q must be odd.

• q must be odd.

• p must be even.

What is the behavior of power functions with integer and non-negative exponents?

• Defined only for positive x.

• Defined only for x equal to zero.

• Defined for all x.

• Defined only for negative x.