Solving Equations with Rational Exponents and Radicals_5.4

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

How do you convert a radical expression to an exponent?

Back

To convert a radical expression to an exponent, use the formula: √(x) = x^(1/2) for square roots, and for nth roots, use: n√(x) = x^(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 for x: 7 + x^(3/2) = 71

Back

x = 16

Front

What is the solution to (2x-8)^(2/3) = 4?

Back

x = 8, x = 0

Front

How do you solve an equation with a fractional exponent?

Back

Raise both sides of the equation to the reciprocal of the fractional exponent to eliminate the exponent.

Front

Solve for x: (3x-5)^(1/4) + 3 = 4

Back

x = 2

Front

What does it mean if an equation has no solution?

Back

It means that there are no values of the variable that satisfy the equation.

Front

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

Back

x = 10

Front

What is the solution to the equation (x+2)^(3/2) = 8?

Back

x = 6