Rational Exponents and Radicals

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

Convert 125^(2/3) to radical form.

Back

The radical form is ∛(125^2).

Front

Evaluate 125^(2/3).

Back

25

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be expressed as roots; for example, x^(m/n) = n√(x^m).

Front

Write ∛(x^7) in exponential form.

Back

x^(7/3).

Front

Evaluate 81^(3/4).

Back

27.

Front

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

Back

It represents the n-th root of x raised to the m-th power.

Front

How do you simplify x^(1/n)?

Back

x^(1/n) is equivalent to the n-th root of x.

Front

What is the value of 64^(2/3)?

Back

16.

Front

Convert 27^(1/3) to radical form.

Back

The radical form is ∛27.