Converting Rational to Radical

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^(1/n) is the nth root of x.

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, √x can be written as x^(1/2).

Front

What is the radicand in a radical expression?

Back

The radicand is the number or expression under the radical sign. For example, in √9, the radicand is 9.

Front

What is the root index in a radical expression?

Back

The root index is the number that indicates which root is being taken. For example, in the square root √x, the root index is 2.

Front

Convert 7^(1/2) to radical form.

Back

7^(1/2) can be expressed as √7.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; the denominator of the exponent indicates the root, while the numerator indicates the power. For example, x^(m/n) = n√(x^m).

Front

How do you express (xy)^(11/4) in radical form?

Back

(xy)^(11/4) can be expressed as the fourth root of (xy)^11, or 4√((xy)^11).

Front

What is the value of 2^(1/3)?

Back

2^(1/3) represents the cube root of 2.

Front

How do you convert a radical expression with an index of n to a rational exponent?

Back

A radical expression with an index of n can be converted to a rational exponent by writing it as x^(1/n). For example, n√x = x^(1/n).

Front

What is the square root of 16 in radical and rational exponent form?

Back

The square root of 16 in radical form is √16, and in rational exponent form, it is 16^(1/2).