Solving Rational Exponents Eqs

Front

Define 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

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

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

Back

x = 2.

Front

Solve: (5x+7)^(1/4) = 3.

Back

x = 74/5 or 14.8.

Front

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

Back

x = 16.

Front

Solve: (6x+2)^(1/3) = 4.

Back

x = 31/3 or 10.3.

Front

What is the first step in solving an equation with a rational exponent?

Back

Isolate the term with the rational exponent on one side of the equation.

Front

How do you eliminate a rational exponent?

Back

Raise both sides of the equation to the power of the denominator of the rational exponent.

Front

What is the importance of checking solutions in rational exponent equations?

Back

Some solutions may not be valid due to the restrictions of the original equation, such as negative bases.

Front

Define the term 'extraneous solution.'

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.