the exponential expression of 2 to the power of 8 has a value of 256. write two other exponential expressions that have a value of 256. ( begin by writing out 2 to the 8th power as the product of 2s. )

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Аноним Аноним · Answer 1 · 2017-09-14T21:08:37+02:00

2^8 = 2*2*2*2*2*2*2*2 = 256

so 4*4*4*4 = 4^4 = 256 also

and another is 16^2 = 256

so the 2 exponentials could be 4^4 and 16^2

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kumaripoojavt kumaripoojavt · Answer 2 · 2022-08-21T14:38:55+02:00

The exponential expressions with value 256 are - [tex]4^{4}[/tex] and [tex]16^{2}[/tex].

We have exponential expression of 2 to the power of 8 has a value of 256.

We have to write two other exponential expressions that have a value of 256.

We can rewrite the above expression as -

[tex](2)^{3x + 4} = 2^{-x}[/tex]

On comparing both sides, we get -

3x + 4 = - x

3x + x = - 4

4x = - 4

x = -1

According to the question -

[tex]2^{8}[/tex] = 256

The above expression can be written as follows -

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256

4 x 4 x 4 x 4 = 256

[tex]4^{4}[/tex] = 256

and

16 x 16 = 256

[tex]16^{2}[/tex] = 256

Hence, the exponential expressions with value 256 are - [tex]4^{4}[/tex] and [tex]16^{2}[/tex].

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https://brainly.com/question/9646383

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