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.

Front

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

Back

√y

Front

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

Back

∛x²

Front

What does the expression ∛x⁷ represent in exponential form?

Back

x^(7/3)

Front

How do you express the square root of a variable in exponent form?

Back

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

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents can be expressed as roots; for example, x^(1/n) is equivalent to the nth root of x.

Front

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

Back

√(4³) or 2²√4.

Front

What is the value of x^(0)?

Back

1, for any non-zero x.

Front

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

Back

∛27 = 3.

Front

What is the formula for converting a rational exponent to radical form?

Back

a^(m/n) = n√(a^m).