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^(m/n) means the n-th root of x raised to the m-th power.

Front

How do you solve x^(3/2) = 27?

Back

To solve x^(3/2) = 27, raise both sides to the power of 2/3: x = 27^(2/3) = 9.

Front

What is the solution set for 2(x-3)^(2/3) - 10 = -2?

Back

The solution set is x = -5 and x = 11.

Front

How do you solve x^(1/4) = 256?

Back

To solve x^(1/4) = 256, raise both sides to the power of 4: x = 256^4 = 16.

Front

What is the solution to (x-2)^(1/5) = -2?

Back

The solution is x = -30.

Front

How do you solve 64x^(3/4) - 125 = 0?

Back

To solve 64x^(3/4) - 125 = 0, isolate x^(3/4) and solve: x = (125/64)^(4/3) = 625/256.

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 n-th root of x.

Front

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

Back

The first step is often to eliminate the rational exponent by raising both sides of the equation to the reciprocal of the exponent.

Front

What does the expression x^(m/n) represent?

Back

The expression x^(m/n) represents the n-th root of x raised to the m-th power.

Front

How do you check your solution after solving an equation with rational exponents?

Back

Substitute your solution back into the original equation to verify that both sides are equal.