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Express as a power with base 4

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)

None of these

answer is D.

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Detailed Solution

Concept- In order to answer this question, let's look at one of the fundamental exponentiation formulas first. if

then,

. After that, we will express the number 16 as a power with base 4 . Then, we will be able to express

easily as a power with base 4 and provide the right response to this query.
Given:
We have to express

as a power with base 4 .
Now, before we proceed we should know that if

. Then,

Now, we will use the above formula to answer this question comfortably.
Now, let

then,

. Then, if we want to express

as a power with base 4 so, we will use the formula from the equation (1). Then,

Now, from the above result, we conclude that the value of

will be equal to

.
Thus, we can express

as a power with base in the form of

.
Hence, correct answer is 4)

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