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.

Tags

CCSS.HSN.RN.A.2

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).

Tags

CCSS.HSN.RN.A.2

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.

Tags

CCSS.8.EE.C.7A

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