Rational Exponents and Radical Form

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

How do you express x^(1/n) in radical form?

Back

x^(1/n) can be expressed as the n-th root of x, written as ∛x.

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be converted to radical form, and vice versa, where a^(m/n) = n√(a^m).

Front

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

Back

27^(1/3) = ∛27.

Front

What is the root index in the expression 12x^(2/3)?

Back

The root index is 3.

Front

Rewrite the expression x^(2/3) in radical form.

Back

x^(2/3) = ∛(x^2).

Front

How do you write the expression ∛(x^7) in exponential form?

Back

∛(x^7) = x^(7/3).

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Front

If a^(m/n) = b, what is the equivalent radical form?

Back

The equivalent radical form is n√(a^m) = b.

Front

Convert the expression (xy)^(11/4) to radical form.

Back

(xy)^(11/4) = 4√((xy)^11).