Solving a radical equation using rational powers with two solutions

The video tutorial covers solving radical equations by expressing rational powers as radicals. It explains the steps to isolate and solve these equations, emphasizing the power rule of exponents. The tutorial also discusses the importance of using absolute values when dealing with even roots and odd powers. Finally, it highlights the need to verify solutions to identify any extraneous results.

What is the first step in solving a radical equation?

• Multiply both sides by the radical

• Convert the equation to a logarithmic form

• Add a constant to both sides

• Isolate the radical or expression with a rational power

How can you simplify an expression with a rational power?

• Multiply by a constant

• Convert it to a logarithm

• Use the power rule of exponents

• Divide by the base

When simplifying an expression with an even root, when should you use absolute value?

• When the index is odd

• When the base is negative

• When the result is a constant

• When the result is an odd power

What is the result of simplifying the 4th root of X to the 12th power?

• X^4

• X^2

• X^3

• X^6

What is the absolute value of 4 cubed?

• 16

• 32

• 64

• 8

What are the solutions to the equation X + 3 to the 2/3 = 4?

• X = 2 and X = -2

• X = 5 and X = -11

• X = 8 and X = -8

• X = 4 and X = -4

What is an extraneous solution?

• A solution that is a complex number

• A solution that does not satisfy the original equation

• A solution that satisfies the original equation

• A solution that is a fraction