Exponents and Radicals Concepts

This lesson covers dividing radicals and rational exponents, focusing on rules for dividing like bases by subtracting exponents. It explains handling negative exponents, simplifying radicals, and dividing expressions with rational exponents. The lesson also includes simplifying complex fractions with roots and concludes with a summary of key concepts.

What is the result of dividing 6^58 by 6^38?

• 6^96

• 6^20

• 6^1

• 6^28

When dividing like bases, what operation is performed on the exponents?

• Multiplication

• Division

• Subtraction

• Addition

What should you do with a negative exponent in a fraction?

• Move it to the denominator

• Ignore it

• Add it to the numerator

• Multiply it by the base

If a term with a negative exponent is in the denominator, where should it be moved?

• To the numerator

• To the left of the fraction

• To the right of the fraction

• It should remain in the denominator

How do you simplify the square root of 24 divided by the square root of 6?

• Square root of 4

• Square root of 2

• Square root of 30

• Square root of 18

What is the result of dividing 20^37 by 4^37?

• 4^37

• 80^37

• 16^37

• 5^37

Why can you divide expressions with the same rational exponent?

• Because they have different bases

• Because they have the same base

• Because they have different exponents

• Because they have the same exponent

How many groups of four can be made from x^15?

• 3 groups

• 4 groups

• 2 groups

• 5 groups

What is the fourth root of 32 x^8 divided by y^12?

• 4x^2/y^3

• 8x^2/y^3

• 16x^2/y^3

• 2x^2/y^3

What should you do if the bases are like but the denominators are different?

• Get a common denominator

• Ignore the denominators

• Add the denominators

• Subtract the denominators