Find the value of

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256.25

answer is D.

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Detailed Solution

Now let us understand the meaning of

times . Hence

is multiplication of the number x, n times. Now let us understand what happens when the power is a fraction. Consider the number

then we have

.
Now to solve equations in indices we have some properties of indices.
Question Image

Hence we use the appropriate identity to solve the equations.
Now consider the given expression

.
Now using the property

we get,

Now we know

and

Hence substituting these values we get,

Now we know that

hence we get,

Now let us factorize 256.
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
256 = 4 × 4 × 4 × 4
Hence we can say that

Hence

So, the correct Ans is “Option 4”.

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