Simplifying Exponential Expressions

The video tutorial covers the quotient property of powers, explaining how to divide powers with the same base by subtracting their exponents. It provides examples using numbers, negative bases, and variables. The tutorial also demonstrates multiplying fractions with exponents and applies these concepts to a real-world problem of predicting population density.

What is the basic rule for dividing powers with the same base?

• Add the exponents

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

In the example 4^5 / 4^2, what is the simplified form?

• 4^1

• 4^7

• 4^3

• 4^2

Why can't the base be zero in the quotient property of powers?

• Because zero raised to any power is zero

• Because division by zero is undefined

• Because zero is not a valid base

• Because it results in a negative exponent

How do you simplify (2^6) / (2^4) using the quotient property?

• 2^2

• 2^10

• 2^1

• 2^4

What is the result of (-7)^9 / (-7)^3 in exponent form?

• (-7)^6

• (-7)^12

• (-7)^9

• (-7)^3

When simplifying H^7 / H^6, what is the result?

• H^6

• H^7

• H^0

• H^1

What is the simplified form of 3^4 * 3^2 / 3^3?

• 3^4

• 3^1

• 3^2

• 3^3

How do you simplify M^8 * M^6 / M^5?

• M^9

• M^14

• M^3

• M^19

In the expression (-4)^9 / (-4)^5 * (-4)^8 / (-4)^2, what is the exponent of the simplified form?

• 14

• 12

• 8

• 10

What is the average number of people per square mile in Tennessee in 2030, given the population is 5 * 5.9^8 and area is 5.9^6?

• 150

• 200

• 174

• 180