Solving Cube Roots and Exponents

The video tutorial explains how to solve an exponential equation where X raised to the X cubed equals 729. The instructor guides viewers through the process of solving the equation by cubing both sides, reviewing exponent rules, and rewriting expressions. The solution involves recognizing 729 as 9 cubed and simplifying the equation to find that X equals the cube root of 9. The tutorial emphasizes understanding exponent manipulation and verifying the solution.

What is the initial equation given in the problem?

• X cubed equals 729

• X raised to the X cubed equals 729

• X raised to the X squared equals 729

• X squared equals 729

What is the first step suggested to solve the equation?

• Add 3 to both sides

• Divide both sides by 3

• Subtract 3 from both sides

• Raise both sides to the third power

What is the result of raising a squared to the third power?

• a to the fifth power

• a to the sixth power

• a to the fourth power

• a to the seventh power

How can the expression X raised to the X cubed raised to the third power be rewritten?

• X raised to the 3 times X cubed

• X raised to the X cubed times 4

• X raised to the X cubed times 2

• X raised to the X squared times 3

What is the cube of 9?

• 81

• 512

• 243

• 729

What is the simplified form of 9 raised to the third power?

• 729

• 243

• 512

• 81

What is the value of X cubed in the simplified equation?

• 81

• 27

• 9

• 3

How do you solve for X when X cubed equals 9?

• Take the square root of 9

• Take the cube root of 9

• Divide 9 by 3

• Multiply 9 by 3

What is the cube root of 9?

• Approximately 2.08

• 4

• 3

• 2

How can you verify the solution to the equation?

• By checking if 9 times 9 equals 81

• By checking if the cube root of 9 raised to the cube root of 9 raised to the third power equals 729

• By checking if the square root of 9 equals 3

• By checking if 9 divided by 3 equals 3