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 represents the power and the denominator represents the root. For example, x^(m/n) means the nth root of x raised to the m power.

Front

How do you convert a radical expression to a rational exponent?

Back

To convert a radical expression to a rational exponent, express the root as a denominator and the power as a numerator. For example, √[n]{x^m} can be written as x^(m/n).

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents and radicals are two ways to express the same mathematical concept. For example, x^(1/n) is equivalent to √[n]{x}.

Front

Convert the expression √[5]{x^3} to a rational exponent.

Back

x^(3/5) is the rational exponent form of √[5]{x^3}.

Front

What is the rational exponent for x^6 when expressed as a radical?

Back

The radical form of x^6 is √[2]{x^{12}}.

Front

How do you express x^(1/10) as a radical?

Back

x^(1/10) can be expressed as √[10]{x}.

Front

What is the rational exponent for √[4]{x^{28}}?

Back

The rational exponent for √[4]{x^{28}} is x^(28/4) or x^7.

Front

How do you simplify the expression x^(m/n)?

Back

To simplify x^(m/n), you can express it as the nth root of x raised to the m power, or √[n]{x^m}.

Front

What is the process for converting x^(3/7) to radical form?

Back

To convert x^(3/7) to radical form, write it as √[7]{x^3}.

Front

What is the general formula for converting a radical to a rational exponent?

Back

The general formula is: √[n]{x^m} = x^(m/n).