Solving Equations with Rational Exponents

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 rational exponent to a radical expression?

Back

To convert a rational exponent to a radical expression, use the formula: a^(m/n) = n√(a^m). For example, x^(3/2) = √(x^3).

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 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 for x: 7 + x^(3/2) = 71. What is x?

Back

x = 16.

Front

What does the equation (6x - 3)^(2/3) + 6 = 15 represent?

Back

It represents a rational exponent equation that can be solved by isolating the term and raising both sides to the power of 3/2.

Front

Solve: (6x - 3)^(2/3) + 6 = 15. What are the possible values of x?

Back

x = 5, x = -4.

Front

What is the significance of checking your solution in rational exponent equations?

Back

Checking your solution is important to ensure that it does not produce extraneous solutions, which can occur when raising both sides of an equation to a power.

Front

How do you handle negative bases with rational exponents?

Back

Negative bases can only be raised to rational exponents that result in a real number. For example, (-x)^(1/2) is not real for negative x.