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.

Front

How do you express the square root of x using rational exponents?

Back

The square root of x can be expressed as x^(1/2).

Front

What is the first step in simplifying a value with a rational exponent?

Back

The first step is to take the root.

Front

If you have x^(m/n), what does m represent?

Back

m represents the power to which the base x is raised.

Front

If you have x^(m/n), what does n represent?

Back

n represents the root that is taken of the base x.

Front

How do you convert x^(1/3) to radical form?

Back

x^(1/3) can be expressed as the cube root of x, or ∛x.

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents provide a way to express roots and powers in a single notation.

Front

Simplify: (x^(1/2))^4

Back

The simplification results in x^(4/2) = x^2.

Front

What is the value of 27^(2/3)?

Back

27^(2/3) = (3^3)^(2/3) = 3^2 = 9.

Front

How do you simplify x^(3/4) * x^(1/4)?

Back

You add the exponents: x^(3/4 + 1/4) = x^(4/4) = x^1 = x.