Question

Write 2^40 as an exponent with a base of: 2^2, 2^5, 2^8, 2^10

Answer 1

240 can be expressed as (22)20, (25)8, (28)5, and (210)4 for the respective bases of 22, 25, 28, and 210 by dividing the exponent 40 by the exponent of the new base.

Step-by-step explanation:

To express 240 with different bases that are powers of 2, we use the property of exponents that allows us to multiply exponents when we raise a power to a power. Since we are given bases that are themselves exponents of 2, we can find equivalent expressions for 240 by dividing the original exponent (40) by the new base's exponent and using the resulting quotient as the new exponent.

• For a base of 22: 240 = (22)20 because 40 / 2 = 20.
• For a base of 25: 240 = (25)8 because 40 / 5 = 8.
• For a base of 28: 240 = (28)5 because 40 / 8 = 5.
• For a base of 210: 240 = (210)4 because 40 / 10 = 4.

Answer 2

2^40 =

1) (2^2)^20

2) (2^5)^8

3) (2^8)^5

4) (2^10)^4

Step-by-step explanation:

We know this simply because we multiply the exponent inside the parentheses by the exponenent outside the parentheses. Using this, we can simply find the numbers that have a product of 40.