Understanding Rational Exponents and Solving Equations

The video tutorial explains how to solve an equation with a rational exponent. It begins by clearing the denominator of the rational exponent and simplifying the equation. The process involves raising both sides to the seventh power, simplifying the exponents, and solving for x by undoing the exponent using the reciprocal power. The tutorial also covers simplifying the right side of the equation using radical form and verifying the solution with a calculator.

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

• Add the denominator to both sides

• Raise both sides to the power of the denominator

• Subtract the numerator from both sides

• Divide both sides by the denominator

When simplifying exponents, what operation is performed when powers are raised to powers?

• Multiplication

• Subtraction

• Division

• Addition

How can you simplify the expression when there is a common factor between the numerator and denominator of an exponent?

• Divide by the common factor

• Multiply the common factor

• Simplify to 1

• Add the common factor

What is the reciprocal power used to undo cubing in an equation?

• One-half

• Three-fourths

• Two-thirds

• One-third

Why do we not include a plus or minus when the exponent is odd?

• Because it makes the equation easier

• Because it is a rule of exponents

• Because there is only one solution

• Because it simplifies the calculation

What is the cube root of 8?

• 4

• 1

• 2

• 3

How do you express eight raised to the power of seven-thirds in radical form?

• As a square root

• As a cube root

• As a fourth root

• As a fifth root

What is the final value of x after solving the equation?

• 123

• 120

• 121

• 122

What operation is performed to isolate x in the final step?

• Multiplication

• Division

• Subtraction

• Addition

How can you verify the solution of the equation using a calculator?

• By checking if the left side equals 9

• By checking if the left side equals 7

• By checking if the left side equals 8

• By checking if the left side equals 6