Dividing Powers with Common Bases

This tutorial explains the division property of exponents, focusing on the quotient of powers property. It demonstrates how to simplify expressions like 4^6 / 4^4 and 3^3 / 3^7 by listing factors and canceling common terms. The key takeaway is that when dividing powers with the same base, you subtract the exponents, performing the subtraction where the highest power is located. The video emphasizes understanding the process through examples and highlights the importance of the base being the same for the property to apply.

What is the result of 4^6 divided by 4^4?

• 4^2

• 16

• 4^10

• 2^4

How do you simplify expressions with the same base being divided?

• By subtracting the exponents

• By dividing the exponents

• By multiplying the exponents

• By adding the exponents

What is the base in the expression 4^6 / 4^4?

• 6

• 4

• 10

• 2

What is the simplified form of 3^3 / 3^7?

• 3^-4

• 3^4

• 1/3^4

• 3^10

In the expression 3^3 / 3^7, which exponent is subtracted from which?

• They are added

• 7 from 3

• They are multiplied

• 3 from 7

What does the quotient of powers property state?

• Divide exponents when dividing powers with the same base

• Subtract exponents when dividing powers with the same base

• Add exponents when dividing powers with the same base

• Multiply exponents when dividing powers with the same base

Where does the subtraction of exponents occur according to the quotient of powers property?

• Where the lower power is located

• Always in the denominator

• Where the higher power is located

• Always in the numerator

What is the result of 3^-4 in terms of a fraction?

• 3^4

• 4/3

• 3/4

• 1/3^4

How can you simplify a power with a negative exponent?

• By converting it into a fraction

• By subtracting it from a positive exponent

• By converting it into a multiplication

• By adding it to a positive exponent

According to the quotient of powers property, what is the simplified form of a^b / a^c when b > c?

• a^(c-b)

• a^(b*c)

• a^(b+c)

• a^(b-c)