Simplifying Exponents and Roots

This video tutorial covers a prerequisite review for accelerated precalculus, focusing on exponent rules and simplifying radicals. It begins with an introduction to exponent rules, including handling negative exponents and the importance of parentheses. The tutorial then transitions to simplifying radicals, demonstrating how to factor and simplify square roots, fourth roots, and cube roots. Each concept is explained with detailed examples to aid understanding.

What is the result of (-2)^2 when the negative sign is outside the exponent?

• 4

• -4

• 8

• -8

How do you simplify 5/2 raised to the power of -2?

• -4/25

• 4/25

• -25/4

• 25/4

What happens to a term with a negative exponent when simplifying an expression?

• It stays in place

• It moves to the denominator

• It moves to the numerator

• It is squared

In the expression 3x^2y^(-3), what is the correct simplification?

• 3x^2y

• 3/x^2y^3

• 3x^2/y^3

• 3x^2y^3

How do you simplify x^(-1)y^(-2) in a fraction?

• x^2/y

• x/y^2

• y^2/x

• 1/x^2y

What is the square root of 80 simplified?

• 2√5

• 8√5

• 16√5

• 4√5

How do you simplify the fourth root of 32?

• 2√2

• 2√3

• 4√2

• 4√3

What is the cube root of 54 simplified?

• 3√9

• 3√6

• 3√3

• 3√2

How do you rationalize the denominator of 3/√8?

• 3/8√2

• 3/4√2

• 3√2/8

• 3√2/4

What is the simplified form of 4√3 * √21?

• 4√7

• 4√63

• 12√21

• 12√7