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: (6x - 3)^(2/3) + 6 = 15. What is x?

Back

x = 5, x = -4.

Front

Solve: (2x - 5)^(1/3) = 3. What is x?

Back

x = 16.

Front

What does it mean to raise a number to a fractional power?

Back

Raising a number to a fractional power means taking a root of the number and then raising it to a power. For example, x^(3/2) means the square root of x cubed.

Front

Solve: (2x - 1)^(3/4) + 9 = 36. What is x?

Back

x = 41.

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related; raising a number to a power and taking a root are opposite operations.

Front

Solve: (x + 2)^(1/2) = 4. What is x?

Back

x = 14.

Front

What is the process to eliminate a rational exponent?

Back

To eliminate a rational exponent, raise both sides of the equation to the reciprocal of the exponent.