Simplifying Exponents and Roots

The video tutorial guides viewers through the process of simplifying a complex algebraic expression involving exponents and radicals. It begins by breaking down the expression into manageable parts, explaining the use of exponent rules and the properties of radicals. The tutorial then demonstrates how to combine and simplify these components, offering different methods for achieving the simplest form. The video concludes with a discussion on the various valid simplifications and the instructor's preferred method.

What is the first step in simplifying the expression r^(2/3) * s^3, all squared?

• Multiply the exponents directly

• Divide the exponents by 2

• Add the exponents

• Take the square root of each term

How can the square root of a number be expressed in terms of exponents?

• As the number raised to the power of 3

• As the number raised to the power of 1/3

• As the number raised to the power of 1/2

• As the number raised to the power of 2

How can 20 be expressed as a product of a perfect square and a non-perfect square?

• 2 * 10

• 5 * 4

• 10 * 2

• 4 * 5

What is the simplified form of s^5 when expressed as a product of a perfect square and a non-perfect square?

• s^2 * s^3

• s^3 * s^2

• s^5

• s^4 * s

What is the result of raising r^4 to the 1/2 power?

• r^4

• r^1

• r^3

• r^2

What is the principal root of 4?

• 1

• 2

• 3

• 4

When combining s^6 and s^2, what is the resulting exponent of s?

• s^3

• s^12

• s^8

• s^4

What is one way to express r^(3 1/3) without using fractional exponents?

• r^3 * cube root of r

• r^4

• r^3 * square root of r

• r^2 * cube root of r

What is the result of combining s^8 and s^(1/2)?

• s^7.5

• s^8

• s^9

• s^8.5

Which of the following is a valid simplification of the expression discussed?

• 2 * s^7.5 * r^(3 1/3) * square root of 5

• 2 * s^9 * r^3 * square root of 5

• 2 * s^8.5 * r^(3 1/3) * square root of 5

• 2 * s^8 * r^3 * square root of 5