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 an integer and the denominator is a positive integer.

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

What is the radical form of x^{1/5}?

Back

The radical form of x^{1/5} is √[5]{x}.

Front

How do you express the cube root of x^8 using a rational exponent?

Back

The cube root of x^8 can be expressed as x^{8/3}.

Front

What is the radical form of x^{1/10}?

Back

The radical form of x^{1/10} is √[10]{x}.

Front

How do you express x^{11/2} in radical form?

Back

x^{11/2} can be expressed in radical form as √(x^{11}).

Front

What is the simplified form of √[3]{x^{15}}?

Back

The simplified form of √[3]{x^{15}} is x^5.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; the denominator of the exponent indicates the root, and the numerator indicates the power.

Front

How do you simplify expressions with rational exponents?

Back

To simplify expressions with rational exponents, apply the laws of exponents, such as multiplying, dividing, and raising powers to powers.

Front

What is the general formula for converting between radical and rational exponent forms?

Back

The general formula is: x^{m/n} = n√(x^m) and n√(x) = x^{1/n}.