Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that can be expressed as a fraction, where the numerator is a power and the denominator indicates the root.

Front

Convert x^(1/2) to radical form.

Back

√x

Front

Convert x^(3/4) to radical form.

Back

∜x^3

Front

Convert x^(1.5) to radical form.

Back

√x^3

Front

Convert y^(1/2) to radical form.

Back

√y

Front

Convert √23 to exponential form.

Back

23^(1/2)

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent both powers and roots; for example, x^(m/n) means the n-th root of x raised to the m-th power.

Front

Convert x^(2/3) to radical form.

Back

∛(x^2)

Front

Convert x^(5/2) to radical form.

Back

√(x^5)

Front

What is the general form of a rational exponent?

Back

x^(m/n) = n√(x^m) or (n√x)^m.