Simplify : ( 1 6 − 2 − 1 3 − 3 ) ÷ 1 5 − 2 Options: A . &nbsp ( 3 5 ) 2 B . &nbsp ( 9 25 ) 2 C . &nbsp ( 5 3 ) 2 D . &nbsp ( 25 9 ) 2

Answer: Option A : A We know that for a non-zero integer a and any integer m , a − m = 1 a m . ∴ 6 − 2 = 1 6 2 ⟹ 1 6 − 2 = 6 2 = 36 Similarly, 1 3 − 3 = 3 3 = 27 and 1 5 − 2 = 5 2 = 25. ⟹ ( 1 6 − 2 − 1 3 − 3 ) ÷ 1 5 − 2 = ( 36 − 27 ) ÷ 25 = 9 25 = 3 2 5 2 = ( 3 5 ) 2 ( ∵ a m b m = ( a b ) m

Simplify :(16−2−13−3)÷15−2

Question

Simplify : $(\frac{1}{6^{- 2}} - \frac{1}{3^{- 3}}) \div \frac{1}{5^{- 2}}$

Options:

A .

(\frac{3}{5})^{2}

B .

(\frac{9}{25})^{2}

C .

(\frac{5}{3})^{2}

D .

(\frac{25}{9})^{2}

Answer: Option A
:
A

We know that for a non-zero integer $a$ and any integer $m,$
$a^{- m} = \frac{1}{a^{m}} .$
$∴ 6^{- 2} = \frac{1}{6^{2}}$
$⟹ \frac{1}{6^{- 2}} = 6^{2} = 36$
Similarly, $\frac{1}{3^{- 3}} = 3^{3} = 27$ and $\frac{1}{5^{- 2}} = 5^{2} = 25.$
$⟹ (\frac{1}{6^{- 2}} - \frac{1}{3^{- 3}}) \div \frac{1}{5^{- 2}} = (36 - 27) \div 25$
$= \frac{9}{25}$
$= \frac{3^{2}}{5^{2}}$
$= (\frac{3}{5})^{2} (∵ \frac{a^{m}}{b^{m}} = (\frac{a}{b})^{m}$