Simplify (25÷28)5 × 2−5.

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Question

Simplify

{(2^{5} \div 2^{8})}^{5}

×

2^{- 5} .

Options:

A . 1210

B . 1220

C . 12(−15)

D . 12(−5)

Answer: Option B
:
B

{(2^{5} \div 2^{8})}^{5} \times 2^{- 5} = {(\frac{2^{5}}{2^{8}})}^{5} \times 2^{- 5}

= {(2^{5 - 8})}^{5} \times 2^{- 5} (∵ \frac{a^{m}}{a^{n}} = a^{m - n})

= {(2^{- 3})}^{5} \times 2^{- 5}

= 2^{- 15} \times 2^{- 5} (∵ (a^{m})^{n} = a^{m n})

= 2^{- 15 - 5} (∵ a^{m} \times a^{n} = a^{m + n})

= 2^{- 20}

= \frac{1}{2^{20}} (∵ a^{- m} = \frac{1}{a^{m}})

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