Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator represents the power and the denominator represents 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 can be converted to radical form, where the denominator of the exponent indicates the root.

Front

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

Back

The simplified form is x^(4/2) = x^2.

Front

What is the value of 8^(2/3)?

Back

8^(2/3) = (cube root of 8)^2 = 2^2 = 4.

Front

How do you multiply two expressions with the same base and rational exponents?

Back

You add the exponents. For example, x^(a/b) * x^(c/d) = x^((ad + bc)/(bd)).