Question

he exponential expression 28 has a value of 256. Write two other exponential expressions that have a value of 256. Explain how you got your answers. (Begin by writing out 2 8as the product of 2s.)

Answer 1

Two other exponents that results in 256 are
`16^2` and
`4^4`

Explanation:

Given

`2^8 = 256`

Required

Write two exponential expression that equals 256

`2^8 = 256`

Expand 8 as 4 * 2

`2^(4*2) = 256`

Using laws of indices, we have

`(2^4)^2 = 256`

2⁴ = 16; So, we have

`16^2 = 256` --- This is one

Recall that

`2^(4*2) = 256`

This can also be rewritten as

`2^(2*4) = 256`

Using laws of indices, we have

`(2^2)^4 = 256`

2² = 4; So, we have

`4^4 = 256` --- This is another one

Hence, two other exponents that results in 256 are
`16^2` and
`4^4`