25. [tex]\(\quad\left(2^5 \div 2^8\right)^5 \times 2^{+5}\)[/tex]

A. [tex]\(2^{-10}\)[/tex]

B. [tex]\(\frac{1}{1024}\)[/tex]

C. Both A and B

D. None of these



Answer :

Let's solve the given mathematical expression step by step:

Given expression: [tex]\(\left(2^5 \div 2^8\right)^5 \times 2^5\)[/tex]

1. Simplify the Division Inside the Parentheses:

The expression inside the parentheses is [tex]\(2^5 \div 2^8\)[/tex].

Using the properties of exponents, this can be simplified as:
[tex]\[ 2^5 \div 2^8 = 2^{5-8} = 2^{-3} \][/tex]

2. Apply the Exponent Outside the Parentheses:

Now, we need to raise [tex]\(2^{-3}\)[/tex] to the power of 5:
[tex]\[ \left(2^{-3}\right)^5 = 2^{-3 \times 5} = 2^{-15} \][/tex]

3. Multiply by [tex]\(2^5\)[/tex]:

Next, we multiply [tex]\(2^{-15}\)[/tex] by [tex]\(2^5\)[/tex]:
[tex]\[ 2^{-15} \times 2^5 = 2^{-15 + 5} = 2^{-10} \][/tex]

4. Evaluate [tex]\(2^{-10}\)[/tex]:

The expression [tex]\(2^{-10}\)[/tex] is equivalent to:
[tex]\[ 2^{-10} = \frac{1}{2^{10}} = \frac{1}{1024} \][/tex]

So, the simplified result is [tex]\(2^{-10}\)[/tex], which is equal to [tex]\(\frac{1}{1024}\)[/tex].

Therefore, the correct answer is:

c. both [tex]\(a\)[/tex] and [tex]\(b\)[/tex]