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^(m/n) means the nth root of x raised to the m power.

Front

Rewrite the expression (2x + 1)^(3/4) without using a radical.

Back

(2x + 1)^(3/4) is already in its simplest form with a rational exponent.

Front

How do you solve the equation (6x - 3)^(2/3) + 6 = 15?

Back

First, isolate the term with the exponent: (6x - 3)^(2/3) = 9. Then raise both sides to the power of 3/2 to eliminate the exponent.

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

If x^(1/n) = a, what is x?

Back

x = a^n, where n is a positive integer.

Front

What does the expression (x^(1/2))^2 simplify to?

Back

x, because raising a power to a power multiplies the exponents.

Front

Solve for x: (x + 2)^(3/2) = 8.

Back

x = 6.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents can be expressed as roots; for example, x^(1/n) is equivalent to the nth root of x.

Front

How do you convert a radical expression to a rational exponent?

Back

For example, √x can be written as x^(1/2).

Front

What is the solution to the equation (x - 1)^(3/4) = 4?

Back

x = 5.