Solving Equations with Fractional Exponents

The video tutorial explains how to solve equations involving variables raised to fractional powers. It begins by introducing the problem and discussing the relationship between radicals and rational exponents. The instructor demonstrates solving the equation by raising both sides to the reciprocal power, ensuring the variable is isolated. Alternative methods using radicals are also explored. The tutorial concludes with a detailed explanation of exponentiation and simplifying expressions, providing multiple approaches to reach the solution.

What is the initial problem presented in the video?

• x cubed equals eight

• x to the three halves equals eight

• x squared equals eight

• x to the one half equals eight

What is the goal when solving the equation x to the three halves equals eight?

• To get x to the fourth power

• To get x to the first power

• To get x to the second power

• To get x to the third power

What is the reciprocal of 3/2?

• 2/3

• 3/2

• 1/2

• 2

What is the result of raising both sides of the equation to the two-thirds power?

• x to the first power

• x to the second power

• x to the third power

• x to the fourth power

How can 8 to the two-thirds power be rewritten as a radical expression?

• Fourth root of 8 squared

• Square root of 8 cubed

• Cube root of 8 squared

• Cube root of 8 cubed

What is the cube root of 64?

• 4

• 16

• 8

• 2

What is another way to solve the equation besides using radical expressions?

• Using trigonometric functions

• Using polynomial equations

• Rewriting the base as an exponent

• Using logarithms

What is 2 cubed?

• 4

• 6

• 8

• 10

What is the final result of 2 squared?

• 2

• 4

• 6

• 8

What is the main reason for using the reciprocal power method?

• To use a calculator

• To simplify the equation

• To isolate x

• To change the base