5.1 nth Roots and Use Rational Exponents

Front

What is the radical form of x^(1/n)?

Back

∛x = x^(1/3) for n=3.

Front

How do you express the nth root of a number in exponential form?

Back

The nth root of a number a is expressed as a^(1/n).

Front

Convert the expression 4^(3/2) into radical form.

Back

√(4^3) = √64 = 8.

Front

What is the value of ∛27?

Back

3, because 3^3 = 27.

Front

If x^(1/2) = 9, what is x?

Back

x = 81, because (9^2) = 81.

Front

Rewrite the expression 5^(2/5) in radical form.

Back

∛(5^2) = ∛25.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, a^(m/n) = n√(a^m).

Front

Solve for x: x^(2/3) = 16.

Back

x = 64, because (16^(3/2)) = 64.

Front

What is the radical form of y^(2/3)?

Back

∛(y^2).

Front

Convert the expression 8^(1/3) into exponential form.

Back

x^(1/3) = 8.