Answer:
Two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]
Step-by-step explanation:
Given
[tex]2^8 = 256[/tex]
Required
Write two exponential expression that equals 256
[tex]2^8 = 256[/tex]
Expand 8 as 4 * 2
[tex]2^{4*2} = 256[/tex]
Using laws of indices, we have
[tex](2^4)^2 = 256[/tex]
2⁴ = 16; So, we have
[tex]16^2 = 256[/tex] --- This is one
Recall that
[tex]2^{4*2} = 256[/tex]
This can also be rewritten as
[tex]2^{2*4} = 256[/tex]
Using laws of indices, we have
[tex](2^2)^4 = 256[/tex]
2² = 4; So, we have
[tex]4^4 = 256[/tex] --- This is another one
Hence, two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]
