Solving Equations with Rational Exponents and Radicals

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: (x - 3)^(1/2) = 4

Back

x - 3 = 16; x = 19.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that make the equation true.

Front

Solve: (2x - 5)^(1/3) = 3

Back

2x - 5 = 27; 2x = 32; x = 16.

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inverses of each other. Raising a number to a power and taking a root are opposite operations.

Front

Solve: x^(1/3) = -1

Back

x = -1.

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: x^(1/2) = 9

Back

x = 81.