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

Answer:

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

Step-by-step 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 $4^4$