Solving Equations with Rational Exponents and Radicals_5.4

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) is the square root of x.

Front

How do you convert a radical expression to an exponent?

Back

To convert a radical expression to an exponent, use the formula: √a = a^(1/2) for square roots, and for nth roots, use: a^(1/n).

Front

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

Back

The first step is to isolate the term with the rational exponent on one side of the equation.

Front

Solve: (3x-5)^(1/4) + 3 = 4. What is x?

Back

x = 2.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that will satisfy the equation.

Front

Solve: (x + 2)^(1/2) - 5 = -2. What is x?

Back

x = 7.

Front

What is the process to eliminate a rational exponent?

Back

Raise both sides of the equation to the power of the denominator of the rational exponent.

Front

Solve: (2x-8)^(2/3) = 4. What are the possible values of x?

Back

x = 8 or x = 0.

Front

What is the significance of checking your solutions in equations with even roots?

Back

Checking solutions is important because even roots can introduce extraneous solutions that do not satisfy the original equation.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.