nth Roots and Rational Exponents

Front

What is an nth root?

Back

An nth root of a number 'a' is a number 'b' such that b^n = a. It is denoted as √[n]{a}.

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, represented as m/n, which indicates both a power and a root.

Front

Convert the expression 16^(1/4) to radical form.

Back

√[4]{16} = 2.

Front

What is the relationship between roots and exponents?

Back

The nth root of a number can be expressed as a fractional exponent: √[n]{a} = a^(1/n).

Front

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

Back

x^(4/2) = x^2.

Front

Convert the expression 27^(2/3) to radical form.

Back

(√[3]{27})^2 = 3^2 = 9.

Front

What is the value of 64^(3/2)?

Back

√[2]{64}^3 = 8^3 = 512.

Front

How do you express a square root using exponents?

Back

The square root of a number 'a' is expressed as a^(1/2).

Front

Simplify: 81^(3/4).

Back

(√[4]{81})^3 = 3^3 = 27.

Front

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

Back

x^(3*2/3) = x^2.