Solving Equations and Exponents

This video tutorial explains how to solve equations with rational exponents. It covers two equations, demonstrating the process of isolating terms, raising both sides to eliminate denominators, and verifying solutions. The tutorial emphasizes understanding the manipulation of exponents and roots, providing a step-by-step guide to solving and verifying the solutions of these equations.

What is the first step in solving an equation with a rational exponent?

• Cube both sides of the equation

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply both sides by the denominator of the exponent

After cubing both sides of the first equation, what is the next step?

• Multiply both sides by a constant

• Take the fifth root of both sides

• Add a constant to both sides

• Take the square root of both sides

What is the result of taking the fifth root of 32,768?

• 12

• 6

• 10

• 8

What is the first step in solving the second equation?

• Subtract 1 from both sides

• Add 1 to both sides

• Multiply both sides by 3

• Divide both sides by 3

What is the next step after isolating the term with the rational exponent in the second equation?

• Take the square root of both sides

• Cube both sides of the equation

• Multiply both sides by 2

• Add a constant to both sides

What is the result of cubing 4 in the second equation?

• 128

• 32

• 16

• 64

Why do we include a plus or minus when taking the square root in the second equation?

• Because the exponent is odd

• To account for two possible solutions

• To simplify the equation

• To eliminate the rational exponent

What are the two solutions for x in the second equation?

• x = 3 and x = -3

• x = 5 and x = -5

• x = 7/2 and x = -9/2

• x = 9/2 and x = -7/2

How do we verify the solutions for the second equation?

• By adding a constant to both sides

• By taking the cube root of both sides

• By multiplying both sides by a constant

• By substituting the solutions back into the original equation

What is the final step in solving the second equation?

• Adding a constant to both sides

• Dividing both sides by 2

• Multiplying both sides by 2

• Subtracting a constant from both sides