Rational Exponents

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^(1/2) is the square root of x.

Front

Convert x^(1/3) to radical form.

Back

∛x

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be expressed in radical form. For example, x^(m/n) = ∛(x^m) where n is the root.

Front

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

Back

x^2

Front

Convert 4^(3/2) to radical form.

Back

√(4^3) = √64 = 8

Front

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

Back

4 (since 8^(2/3) = (∛8)^2 = 2^2 = 4)

Front

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

Back

√(x^5) or (x^5)^(1/2) = √(x^5) = x^(5/2)

Front

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

Back

x^2

Front

Convert 27^(1/3) to exponential form.

Back

x^(1/3) = 3.

Front

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

Back

8 (since 16^(3/4) = (√16)^3 = 4^3 = 64)