Solving Equations with Rational Exponents

The video tutorial explains how to solve equations with rational exponents, focusing on eliminating the fractional part of the exponent. The instructor demonstrates the method using an example equation, x to the three-halves equals 27, and provides a step-by-step solution. The key strategy is to first eliminate the denominator of the exponent by raising both sides of the equation to the power of the denominator. The video concludes with general tips for solving similar equations.

What is a rational exponent?

• An exponent that is a fraction

• An exponent that is a whole number

• An exponent that is negative

• An exponent that is zero

In the example x^(3/2) = 27, what is the first step to solve for x?

• Multiply both sides by 2

• Take the square root of both sides

• Square both sides

• Divide both sides by 3

Why do we square both sides in the equation x^(3/2) = 27?

• To convert the equation to a linear form

• To find the value of x directly

• To make the equation simpler

• To eliminate the fraction in the exponent

What happens to the exponent when you square x^(3/2)?

• It becomes x^3

• It becomes x^(9/4)

• It becomes x^(3/4)

• It becomes x^6

What is the exponent of x after squaring x^(3/2)?

• x^(3/4)

• x^2

• x^(9/4)

• x^3

If you have x^(3/4), what power should you raise it to eliminate the denominator?

• Raise to the 3rd power

• Raise to the 4th power

• Raise to the 2nd power

• Raise to the 5th power

After simplifying x^3 = 27^2, what is the next step?

• Divide both sides by 27

• Take the square root of both sides

• Take the cube root of both sides

• Multiply both sides by 3

What is the cube root of 27?

• 2

• 3

• 4

• 5

What is the final value of x in the equation x^(3/2) = 27?

• 9

• 15

• 6

• 12

What is the result of 27 squared?

• 243

• 54

• 81

• 729