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Q.

The value of (256)0.16(256)0.09 is

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a

16

b

64

c

256.25

d

4

answer is D.

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Detailed Solution

The question is asking to calculate the value of (256)0.16 × (256)0.09, and the solution involves simplifying the expression using the laws of exponents.

Detailed Explanation

Given Expression:

(256)0.16 × (256)0.09

Step 1: Apply the Law of Exponents

The law of exponents states that for a common base:

am × an = am+n

Here, the base 256 is common, so the exponents 0.16 and 0.09 can be added:

(256)0.16 × (256)0.09 = (256)0.16 + 0.09

Step 2: Add the Exponents

0.16 + 0.09 = 0.25

So, the expression becomes:

(256)0.25

Step 3: Simplify the Exponent

The exponent 0.25 can be rewritten as 1/4:

(256)0.25 = (256)1/4

Step 4: Find the Fourth Root of 256

The fourth root of 256 is:

4(256) = 4

Final Answer:

The value of (256)0.16 × (256)0.09 is:4

Explanation

The image shows the detailed steps of solving (256)0.16 × (256)0.09:

  1. Combine Exponents:The exponents 0.16 and 0.09 are added using the law of exponents:(256)0.16 × (256)0.09 = (256)0.25
  2. Rewrite the Exponent:The exponent 0.25 is expressed as 1/4, leading to:(256)0.25 = (256)1/4
  3. Simplify the Root:The fourth root of 256 is calculated as:4(256) = 4

Thus, the final value is 4.

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