Exponential Functions with Radical Bases: Assignment

Explain why the square root of a number is defined to be equal to that number to the 1/2 power.

(Put this in your own words) Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Which functions are equivalent to f(x)=∜162^x? Check all that apply.

1, 2, and 5

Which exponential functions have been simplified correctly? Check all that apply.

1, 3, and 4

Simplify the function f(x)=1/3(81)^3x/4. Then determine the key aspects of the function.

13, 27, all real numbers, y>0

What is the base of the exponent in the function f(x)=3(∛8)^2x when the function is written using only rational numbers and is in simplest form?

4

Determine the domain and range of the function f(x)=2∛108^2x.

A. (x | all real numbers ); ( | y>0 )

Which is equivalent to (∛125)^x?

A. 125^1/3x

Which expression is equivalent to 81^1/3?

A. 3∛3

Determine which function produces the same graph as f(x)=(8^2/3x)(16^1/2x).

B. 4^2x

Which graph represents the function f(x)=8^1/3x?

B. Second Graph

How are the functions f(x)=16^x and g(x)=16^1/2x related?

C. The output values of g(x) are the square root of the output values of f(x) for the same value of x.