Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(m/n) means the nth root of x raised to the mth 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 value of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero is equal to 1. For example, x^0 = 1.

Front

How do you express the cube root of x^7 using a rational exponent?

Back

The cube root of x^7 can be expressed as x^(7/3).

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^(m/n) can be expressed as the nth root of x raised to the mth power, or √[n]{x^m}.

Front

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

Back

x^(11/2) can be expressed as √[2]{x^{11}}.

Front

What is the simplified form of √[5]{x^3} using a rational exponent?

Back

The simplified form of √[5]{x^3} using a rational exponent is x^(3/5).

Front

How do you simplify √[n]{x^m}?

Back

To simplify √[n]{x^m}, express it as x^(m/n).

Front

What is the value of x^(6) when x = 2?

Back

When x = 2, x^(6) = 2^6 = 64.

Front

What does the expression x^(1/n) represent?

Back

The expression x^(1/n) represents the nth root of x.