Evaluating Powers of Rational Numbers

The video tutorial explains how to evaluate expressions with given variable values, focusing on y squared, q cubed, and d to the fourth. It demonstrates two methods for each: expanding and using the properties of exponents. The tutorial emphasizes the importance of parentheses in calculations and verifies results using a graphing calculator.

What is the first step in evaluating an expression for a given variable value?

• Substitute the given value into the expression

• Divide the variable by the given value

• Multiply the variable by itself

• Add the variable to itself

When evaluating y squared for y = -2/7, what is the result of the numerator after expansion?

• 49

• 7

• 4

• 2

What is the result of y squared when y = -2/7?

• -4/49

• 4/49

• -2/7

• 2/7

How many factors of negative two-thirds are used when evaluating q cubed?

• Two

• Three

• Four

• One

What is the result of q cubed when q = -2/3?

• -8/27

• 8/27

• -2/3

• 2/3

What is the result of the numerator when evaluating d to the fourth for d = -4/3 using expansion?

• 81

• 256

• 16

• 64

What is the result of d to the fourth when d = -4/3?

• 81/256

• -256/81

• -81/256

• 256/81

What is the purpose of using a graphing calculator in this context?

• To find the derivative

• To plot graphs

• To verify the results of manual calculations

• To solve equations

What is the result of the square of negative 2/7 on a graphing calculator?

• 49/4

• -4/49

• 4/49

• 2/7

What is the result of the cube of negative 2/3 on a graphing calculator?

• -8/27

• 8/27

• 2/3

• -2/3