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. For example, x^(1/n) is a rational exponent.

Front

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

Back

To convert a rational exponent to a radical expression, use the formula: x^(m/n) = n√(x^m), where m is the numerator and n is the denominator.

Front

Convert x^(1/8) to a radical expression.

Back

x^(1/8) = 8√(x).

Front

Convert x^(11/2) to a radical expression.

Back

x^(11/2) = √(x^11).

Front

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

Back

To convert a radical expression to a rational exponent, use the formula: n√(x^m) = x^(m/n), where m is the power and n is the root.

Front

Convert √[3]{x^6} to a rational exponent.

Back

√[3]{x^6} = x^(6/3) = x^2.

Front

Convert √[3]{x^7} to a rational exponent.

Back

√[3]{x^7} = x^(7/3).

Front

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

Back

√[5]{x^3} = x^(3/5).

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent both powers and roots, where the denominator of the exponent indicates the root and the numerator indicates the power.

Front

If x^(1/n) = n√(x), what does x^(m/n) equal?

Back

x^(m/n) = n√(x^m).