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

True

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False

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Solution

The correct option is A
True

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

= $(\frac{4^{- 7}}{4^{- 10}}) \times 4^{- 5}$
= $4^{- 7 + 10} \times 4^{- 5} (∵ \frac{a^{m}}{a^{n}} = a^{m - n})$
$= 4^{3} \times 4^{- 5}$
$\Rightarrow 4^{3 - 5} (∵ a^{m} \times a^{n} = a^{m + n})$
$= 4^{- 2} = \frac{1}{4^{2}}$
$= \frac{1}{16}$
$= 16^{- 1}$

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Similar questions

The value of ( $4^{- 7} \div 4^{- 10}) \times 4^{- 5}$ is $16^{- 1}$ .

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

S = 1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . .

S = 1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + \dots \infty .

S

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