Divisibility and Exponential Expressions

The video tutorial explores whether the expression 2^9 - 2^7 is divisible by 3 using two methods. The first method involves factoring out common terms to show divisibility by 3. The second method uses a calculator to evaluate the expression and checks the sum of the digits for divisibility by 3. Both methods confirm that the expression is divisible by 3.

What is the common factor in the expression 2^9 - 2^7?

• 3

• 2^7

• 1

• 2^2

How can the expression 2^9 - 2^7 be rewritten to show divisibility by 3?

• As 2^9 - 2^7

• As 3 * 2^7

• As 2^2 * 2^7

• As 4 * 2^7

What is the result of 2^2 - 1 in the factorization method?

• 1

• 4

• 2

• 3

What is the sum of the digits of 384, the evaluated expression?

• 18

• 15

• 12

• 21

Why is the number 384 considered divisible by 3?

• Because it ends in 4

• Because it is even

• Because the sum of its digits is divisible by 3

• Because it is a multiple of 2