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^(m/n) means the nth root of x raised to the m power.

Front

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

Back

√x

Front

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

Back

√(x^3)

Front

Convert x^(5/4) to radical form.

Back

∜(x^5)

Front

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

Back

∛(x^2)

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents provide a way to express roots using exponents. For example, x^(1/n) is equivalent to the nth root of x.

Front

Write the expression in exponential form: ∜(x^6)

Back

x^(6/4) or x^(3/2)

Front

Write the expression in exponential form: ∛(y^9)

Back

y^(9/3) or y^3

Front

What is the formula for converting a radical expression to an exponent?

Back

The formula is: a^(1/n) = ∛a, where n is the index of the root.

Front

Convert the expression ∜(16) to exponential form.

Back

16^(1/4)