Radicals and Rational Exponents

Front

What is a radical?

Back

A radical is a symbol used to indicate the root of a number, most commonly the square root.

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a root and a power.

Front

Simplify: √64

Back

8

Front

Simplify: 2^(3/2)

Back

√(2^3) = √8 = 2√2

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed as rational exponents; for example, √x = x^(1/2).

Front

Simplify: 5^(2/3)

Back

(5^2)^(1/3) = √(25) = 5.

Front

What does the expression x^(m/n) represent?

Back

It represents the n-th root of x raised to the m-th power.

Front

Simplify: (27)^(1/3)

Back

3

Front

What is the value of 16^(3/4)?

Back

(16^(1/4))^3 = 2^3 = 8.

Front

Simplify: 81^(1/4)

Back

3.