Learn how to rewrite and simplify an expression raised to a rational power

The video tutorial explains how to express 27 to the one-third power as a radical expression. It covers the conversion of exponents to radical form, focusing on cube roots. The tutorial also discusses the concept of cube roots, explaining how to determine the number that, when multiplied by itself three times, equals 27. Additionally, it introduces prime factorization as a method to simplify expressions.

What does the denominator in a fractional exponent represent when converting to a radical expression?

• The index of the root

• The base of the expression

• The exponent of the radicand

• The radicand

What is the cube root of 27?

• 81

• 9

• 27

• 3

How can you simplify a cube root if you don't know the number that multiplies by itself three times to give the original number?

• By using addition

• By using division

• By using prime factorization

• By using subtraction

What is the result of 27 raised to the first power?

• 1

• 3

• 9

• 27

What is a possible method to derive explicit answers in radical expressions?

• Using division

• Using multiplication

• Using simplification

• Using approximation