Converting Rational to Radical

Front

What is a rational exponent?

Back

A rational exponent is an exponent that can be expressed as a fraction, where the numerator is the power and the denominator is 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 in a fraction. For example, √x = x^(1/2) and ∛x = x^(1/3).

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots. For example, x^(1/n) is equivalent to the nth root of x.

Front

Convert the expression √(xy) to a rational exponent.

Back

(xy)^(1/2)

Front

Convert the expression ∛(x^2) to a rational exponent.

Back

(x^2)^(1/3)

Front

What is the general form of converting a radical to a rational exponent?

Back

The general form is: n√(a) = a^(1/n), where n is the degree of the root.

Front

How do you simplify the expression (x^(1/2))^4?

Back

Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^2.

Front

What happens to the exponent when you cross the fraction bar in a rational exponent?

Back

The sign of the exponent changes. For example, x^(-m/n) = 1/(x^(m/n)).

Front

Convert the expression (xy)^(3/4) to radical form.

Back

√[4]{(xy)^3}

Front

What is the exponential form of the expression 1/(x^(1/2))?

Back

x^(-1/2)