Rational Exponents and Radicals

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(m/n) means the n-th root of x raised to the m-th 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 fraction. For example, √x can be written as x^(1/2) and ∛x as x^(1/3).

Front

Simplify: 2^(6/3)

Back

8

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related. The n-th root of a number can be expressed as raising that number to the power of 1/n.

Front

Simplify: 4^(3/2)

Back

8

Front

What is the value of 8^(2/3)?

Back

4

Front

How do you simplify expressions with rational exponents?

Back

To simplify expressions with rational exponents, convert them to radical form if necessary, apply the laws of exponents, and simplify the resulting expression.

Front

What is the value of 27^(1/3)?

Back

3

Front

Simplify: (x^(1/2))^4

Back

x^2

Front

What is the value of 16^(3/4)?

Back

8