Rational Exponents & 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 nth root of x raised to the m power.

Front

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

Back

√x

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be expressed as radicals. For example, x^(m/n) = n√(x^m).

Front

Simplify: x^(2/3) * x^(1/3)

Back

x^(1) or x.

Front

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

Back

2^(3/2) = √(2^3) = √8 = 2√2.

Front

Convert 4^(1/2) to radical form.

Back

√4 = 2.

Front

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

Back

x^(2) or x^2.

Front

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

Back

3, because 3^3 = 27.

Front

Convert x^(5/2) to radical form.

Back

√(x^5) or x^2√x.

Front

Simplify: (x^(1/3) * y^(1/3))^3

Back

xy.