standard_description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^(3) = 5(^(1/3))^(3) to hold, so (5^(1/3))^(3) must equal 5.
problem_activity: Problem 1
Consider the statement: A negative number raised to any whole number power will be negative.
Is this statement always, sometimes, or never true? Justify your response.
Problem 2
Consider the statement: An odd number raised to an odd power will be odd.
Is this statement always, sometimes, or never true? Justify your response.
Problem 3
What is the last digit of
$${7^{2023}}$$
? Explain.


aligns: no