Simplifying Roots and Exponents

The video tutorial explains how to simplify the 18th root of 27 raised to the 6th power using rational exponents. It demonstrates converting the expression into a rational exponent form and simplifying it to 27 raised to the power of 1/3. The tutorial explores different methods, including recognizing 27 as a perfect cube and using prime factorization, to simplify the expression to 3. The video concludes by summarizing the various approaches to achieve the simplification.

What is the initial expression we are trying to simplify?

• The 6th root of 18 raised to the 27th power

• The 18th root of 27 raised to the 6th power

• The 18th root of 6 raised to the 27th power

• The 27th root of 18 raised to the 6th power

How can the nth root of a number raised to the mth power be expressed?

• As a rational exponent with m as the numerator

• As a rational exponent with n as the denominator

• As a rational exponent with n as the numerator

• As a rational exponent with m as the denominator

What does the expression 27^(6/18) simplify to?

• 27^(1/18)

• 27^(1/3)

• 27^(1/2)

• 27^(1/6)

What is the cube root of 27?

• 3

• 2

• 4

• 5

What is the prime factorization of 27?

• 3 * 3 * 2

• 3 * 3 * 3

• 2 * 2 * 3

• 2 * 3 * 3

How can 27^(1/3) be rewritten using radicals?

• As the fifth root of 27

• As the fourth root of 27

• As the square root of 27

• As the cube root of 27

What is the result of simplifying the 18th root of 3^18?

• 27

• 9

• 3

• 1

What is the exponent when 3^3 is raised to the power of 1/3?

• 0

• 1

• 2

• 3

What is the simplified form of 3^(3*1/3)?

• 3^3

• 3^2

• 3^1

• 3^0

What is the final simplified result of the original expression?

• 3

• 4

• 2

• 1