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 solve an equation with a rational exponent?

Back

To solve an equation with a rational exponent, isolate the variable and then raise both sides of the equation to the reciprocal of the rational exponent.

Front

What is the reciprocal of 1/5?

Back

The reciprocal of 1/5 is 5.

Front

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

Back

x = -30.

Front

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

Back

x = 127.

Front

What is the cube root of 54?

Back

The cube root of 54 is approximately 3.78.

Front

Solve for x: 2x^(3/4) = 54

Back

x = 81.

Front

What is the fourth root of 256?

Back

The fourth root of 256 is 4.

Front

Solve for x: x^(1/4) = 256

Back

x = -4 or x = 4.

Front

What is the solution to the equation 2x^3 - 10 = 442?

Back

x = 6.