Simplify an expression by applying quotient rule of exponents

The video tutorial begins with an analogy to introduce the topic of exponents. It explains the quotient rule, comparing it to the product rule, and highlights common mistakes in dividing fractions. The tutorial then demonstrates how to simplify fractions and apply exponent rules, including handling negative exponents, to solve mathematical problems.

What is the main idea behind the quotient rule in exponents?

• Dividing powers when dividing exponents with the same base

• Multiplying powers when dividing exponents with the same base

• Subtracting powers when dividing exponents with the same base

• Adding powers when dividing exponents with the same base

When simplifying the fraction 4/18, what is the correct simplified form?

• 1/2

• 2/9

• 4/9

• 1/3

What is a common mistake when simplifying fractions?

• Dividing the numerator and denominator by different numbers

• Not simplifying the fraction at all

• Multiplying the numerator and denominator by the same number

• Adding the numerator and denominator

How do you handle a negative exponent in the numerator?

• Multiply it by the denominator

• Add it to the denominator

• Move it to the denominator to make it positive

• Leave it as is

What is the final simplified expression for the given problem?

• 2X^4 / 9Y^7

• 2Y^7 / 9X^4

• 9X^4 / 2Y^7

• 9Y^7 / 2X^4