Tag: number names, numerals and place values

$829030000=K \times 10^8$

$\displaystyle 108=2\times 2\times  3\times 3\times 3=2^{2}\times 3^{3}$
$\displaystyle 192=2\times2\times2\times2\times2\times2\times3$
$\displaystyle =2^{6}\times 3^{1}$
$\displaystyle 108 \times 192=2^{2}\times 3^{3}\times 2^{6}\times 3^{1}$
$\displaystyle =2^{8}\times 3^{4}$
Sum of the powers = 8 + 4 = 12

$\displaystyle (243)^{-2/5} =\displaystyle(3^5)^{-2/5}$
                $\displaystyle = 3^{-2} = \frac{1}{9}$

$\displaystyle (64)^{-2/3} = 4^3 \times 1^{-2/3} = 4^{-2}$
                 $\displaystyle = \frac{1}{4^2} = \frac{1}{16}$   

$[(-3)^{(-2)}]^{(-3)} = (-3)^6$
                           = 729

$0.0000000000000000000016=\displaystyle \frac{16}{100000000000000000000}$

$(3^0 - 2^1) \times 4^2 = (1-2) \times 16$
                                         $= -1 \times 16 = -16$

$\displaystyle \frac{(27)^{-2/3}}{ ( 64)^{-2/3}} = \frac{\displaystyle \frac{1}{9}}{ \displaystyle \frac{14}{16}} = \frac{16}{9}$

$\displaystyle 6\cdot 8793\times 10^{4}=68,793$