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 for x: (x + 3)^(1/2) = 4

Back

x = 13.

Front

What does the equation (2x - 5)^(1/3) = 3 represent?

Back

It represents that the cube root of (2x - 5) equals 3, which can be solved by cubing both sides.

Front

How do you eliminate a rational exponent in an equation?

Back

You can eliminate a rational exponent by raising both sides of the equation to the reciprocal of the exponent.

Front

Solve for x: (x - 1)^(3/4) = 8

Back

x = 513.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent both powers and roots; the denominator of the exponent indicates the root.

Front

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

Back

x = 43/3.

Front

What is the importance of checking your solution in equations with rational exponents?

Back

It's important to check your solution because raising to a power can introduce extraneous solutions that do not satisfy the original equation.