Division Properties of Exponents Explained

The video tutorial covers division properties of exponents, including how to divide powers with the same base and raise a quotient to a power. It explains simplifying expressions using exponent rules, applying these rules to scientific notation for calculating population density, and handling negative exponents. The tutorial also demonstrates raising quotients to a power and provides various techniques for simplifying expressions.

What is the result of dividing two powers with the same base?

• Subtract the exponents

• Add the exponents

• Multiply the exponents

• Divide the exponents

If you have a power with a negative exponent, where should it be moved?

• To the bottom of the fraction

• To the top of the fraction

• It is eliminated

• It remains unchanged

How do you handle a power with a fractional exponent when dividing?

• Add using a common denominator

• None of the above

• Subtract using a common denominator

• Multiply the exponents

What is the simplified form of x^6 / x^2?

• x^12

• x^4

• x^8

• x^3

How do you simplify an expression with a negative exponent?

• Convert it to a positive exponent without moving

• Leave it as is

• Move it to the opposite part of the fraction

• None of the above

What is the population density if the population is 1.21 x 10^7 and the area is 4.81 x 10^5 square miles?

• 25 people per square mile

• 250 people per square mile

• 2.5 people per square mile

• 0.25 people per square mile

How do you simplify (x/y)^3?

• x^3 + y^3

• x / y^3

• x^3 * y^3

• x^3 / y^3

What happens when you raise a quotient to a power?

• Only the numerator is raised to the power

• The power is divided between the numerator and denominator

• Both the numerator and denominator are raised to the power

• Only the denominator is raised to the power

What is the result of 4^2 / x^6 when simplified?

• 16 x^6

• 16 / x^6

• 16 x^12

• 4 / x^12

How do you simplify a^(-3/4) to the fifth power?

• a^(12/20)

• a^(-12/20)

• a^(15/4)

• a^(-15/4)