Solving Equations with Rational Exponents

The video tutorial explains how to solve an equation with a fractional exponent by first clearing the exponent through cubing both sides. It then demonstrates undoing the squaring by taking the square root or using rational exponents, highlighting the need for a plus or minus sign due to the even exponent. The tutorial finds two solutions for x and verifies them by substituting back into the original equation, confirming the solutions using a calculator.

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

• Multiply both sides by the denominator of the exponent

• Add the same number to both sides

• Raise both sides to the power of the denominator of the exponent

• Subtract the same number from both sides

When simplifying the left side of the equation, what operation is performed?

• Addition

• Multiplication

• Squaring

• Subtraction

What is the result of cubing the number 4?

• 128

• 64

• 32

• 16

How can we undo the squaring of a term in an equation?

• By adding a constant

• By subtracting a constant

• By taking the square root

• By multiplying by two

Why do we consider both positive and negative solutions when solving the equation?

• Because squaring a number can result in a positive value for both positive and negative inputs

• Because the equation is quadratic

• Because the equation is cubic

• Because the equation is linear

What is the reciprocal power of 2 used in the solution process?

• 1

• 1/2

• 2

• 3

What operation is performed to isolate x in the equation?

• Adding 3 to both sides

• Dividing both sides by 3

• Subtracting 3 from both sides

• Multiplying both sides by 3

What are the two solutions obtained for x?

• 9 and -7

• 12 and -4

• 10 and -6

• 11 and -5

How do we verify the solutions of the equation?

• By solving a different equation

• By using a calculator to check the solutions

• By graphing the equation

• By substituting the solutions back into the original equation

What is the result when substituting x = 11 back into the original equation?

• 2

• 3

• 4

• 5