The value of ( 4 − 7 ÷ 4 − 10 ) × 4 − 5 is 16 − 1 . Options: A . &nbsp True B . &nbsp False C . &nbsp 257 16 D . &nbsp 271 18

Answer: Option A : A The value of ( 4 − 7 ÷ 4 − 10 ) × 4 − 5 is 16 − 1 . ( 4 − 7 ÷ 4 − 10 ) × 4 − 5 = ( 4 − 7 4 − 10 ) × 4 − 5 = 4 − 7 + 10 × 4 − 5 ( ∵ a m a n = a m − n ) = 4 3 × 4 − 5 ⇒ 4 3 − 5 ( ∵ a m × a n = a m + n ) = 4 − 2 = 1 4 2 = 1 16 = 16 − 1

The value of (4−7 ÷ 4−10 ) × 4−5 is 16−1

Question

The value of ( $4^{- 7}$ ÷ $4^{- 10}$ ) × $4^{- 5}$ is $16^{- 1}$ .

Options:

A . True

B . False

C .

\frac{257}{16}

D .

\frac{271}{18}

Answer: Option A
:
A

The value of ( $4^{- 7}$ ÷ $4^{- 10}$ ) × $4^{- 5}$ is $16^{- 1}$ .
$(4^{- 7}$ ÷ $4^{- 10}) \times 4^{- 5}$
= $(\frac{4^{- 7}}{4^{- 10}}) \times 4^{- 5}$
= $4^{- 7 + 10} \times 4^{- 5} (∵ \frac{a^{m}}{a^{n}} = a^{m - n})$
$= 4^{3} \times 4^{- 5}$
$\Rightarrow 4^{3 - 5} (∵ a^{m} \times a^{n} = a^{m + n})$
$= 4^{- 2} = \frac{1}{4^{2}}$
$= \frac{1}{16}$
$= 16^{- 1}$