Roots and Exponents Simplification

The video tutorial explains how to simplify radicals without using a calculator. It covers the process of finding cube roots and fourth roots, including those of negative numbers and fractions. The tutorial demonstrates how to use factor trees to simplify expressions and how to handle exponents in conjunction with roots.

What is the result of squaring the cube root of -27?

• -9

• 9

• -3

• 3

If you take the cube root of -8 and raise it to the fifth power, what is the result?

• 16

• -16

• 32

• -32

How do you simplify the fourth root of a fraction?

• Divide the fraction by 4

• Square the fraction

• Take the fourth root of both the numerator and the denominator

• Multiply the numerator and denominator by 4

What is the fourth root of 81?

• 4

• 9

• 3

• 2

What is the result of simplifying 1 over 81 to the one-fourth power?

• 1/9

• 1/81

• 1/3

• 1/27

What is the fourth root of 16?

• 16

• 8

• 2

• 4

What is the result of cubing the fourth root of 16?

• 2

• 8

• 16

• 4

What is the fourth root of 81, and what is its cube?

• 3 and 9

• 3 and 27

• 9 and 27

• 9 and 81

What is the result of simplifying 16 over 81 to the three-fourths power?

• 16/81

• 2/3

• 8/27

• 4/9

What is the process to simplify expressions with fractional exponents?

• Add the exponents

• Subtract the exponents

• Find the root indicated by the denominator and then raise to the power of the numerator

• Multiply the exponents