Question

Задания (2 3 4) с (g по l)
Вычислите пожалуйста не сократите а вычислите очень срочно хееелпп!!!!!!

Answer 1

Ответ:

Применяем свойства степеней :   $\bf a^{k}=\underbrace{\bf a\cdot a\cdot ...\cdot a}_{k}\ \ ,\ \ a^{-1}=\dfrac{1}{a}\ \ ,$  

     $\bf (a^{k})^{n}=a^{k\cdot n}$     .  

$\bf 2)\ \ 0,12^2=0,12\cdot 0,12=0,0144\\\\0,01^3=0,01\cdot 0,01\cdot 0,01=0,000001\\\\1,9^2=1,9\cdot 1,9=3,61\\\\0,06^3=0,06\cdot 0,06\cdot 0,06=0,000216\\\\0,15^2=0,15\cdot 0,15=0,0225\\\\0,2^4=0,2\cdot 0,2\cdot 0,2\cdot 0,2=0,0016$    

$\bf 3)\ \ 3^{-3}=(3^{-1})^3=\Big(\dfrac{1}{3}\Big)^3=\dfrac{1}{3}\cdot \dfrac{1}{3}\cdot \dfrac{1}{3}=\dfrac{1}{27}\\\\2^{-5}=(2^5)^{-1}=(2\cdot 2 \cdot 2\cdot 2\cdot2)^{-1}=32^{-1}=\dfrac{1}{32}\\\\(\sqrt2)^{-4}=\Big((\sqrt2)^4\Big)^{-1}=\Big(\sqrt2\cdot \sqrt2 \cdot \sqrt2\cdot \sqrt2\Big)^{-1}=4^{-1}=\dfrac{1}{4}\\\\\Big(\dfrac{12}{5}\Big)^{-1}=\dfrac{5}{12}\\\\13^{-1}=\dfrac{1}{13}\\\\4^{-3}=(4\cdot 4\cdot 4)^{-1}=64^{-1}=\dfrac{1}{64}$  

$\bf 4)\ \ -0,04^2=-(0,04^2)=-(0,04\cdot 0,04)=-0,0016\\\\-\Big(\dfrac{4}{5}\Big)^2=-\Big(\dfrac{4}{5}\cdot \dfrac{4}{5}\Big)=-\dfrac{16}{25}\\\\(-0,2)^3=(-0,2)\cdot (-0,2)\cdot (-0,2)=-0,008\\\\-3^3=-(3^3)=-(3\cdot 3\cdot 3)=-27\\\\(-0,1)^2=(-0,1)\cdot (-0,1)=0,01\\\\-\Big(\dfrac{1}{5}\Big)^3=-\Big(\dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\Big)=-\dfrac{1}{125}$                  

Answer 2

2

$g) \: {0.12}^{2} = 0.12 \times 0.12 = 0.0144 \\ h) \: {0.01}^{3} = 0.01 \times 0.01 \times 0.01 = 0.000001 \\ i) \: {1.9}^{2} = 1.9 \times 1.9 = 3.61 \\ j) \: 0.06 {}^{3} = 0.06 \times 0.06 \times 0.06 = 0.000216 \\ k) \: 0.15 {}^{2} = 0.15 \times 0.15 = 0.0225 \\ l) \: {0.2}^{4} = 0.2 \times 0.2 \times 0.2 \times 0.2 = 0.0016$

3

$g) \: {3}^{ - 3} = ( {3}^{ - 1} ) {}^{3} = ( \frac{1}{3} ) {}^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27} \\ h) \: {2}^{ - 5} = ( {2}^{ - 1} ) {}^{5} = ( \frac{1}{2} ) {}^{5} = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{32} \\ i) \: \sqrt{2} {}^{ - 4} = ( (\sqrt{2} ) {}^{4} ) {}^{ - 1} = ( {2}^{2} ) {}^{ - 1} = {4}^{ - 1} = \frac{1}{4} \\ j) \: ( \frac{12}{5} ) {}^{ - 1} = \frac{5}{12} \\ k) \: {13}^{ - 1} = \frac{1}{13} \\ l) \: {4}^{ - 3} = ( {4}^{ - 1} ) {}^{3} =( \frac{1}{4} ) {}^{3} = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64}$

3

$g) \: - 0.04 {}^{2} = -( 0.04 \times 0.04) = - 0.0016 \\ h) \: - ( \frac{4}{5} ) {}^{2} = - ( \frac{4}{5} \times \frac{4}{5} ) = - \frac{16}{25} \\ i) \: ( - 0.2) {}^{3} = - 0.2 \times ( - 0.2) \times ( - 0.2) = - 0.008 \\ j) \: - 3 {}^{3} = - (3 \times 3 \times 3) = - 27 \\ k) \: ( - 0.1) {}^{2} = - 0.1 \times ( - 0.1) = 0.01 \\ l) \: - ( \frac{1}{5} ) {}^{3} = - ( \frac{1}{5} \times \frac{1}{5} \times \frac{1}{5} ) = - \frac{1}{125}$