Rešite left(100*10right)^-3sqrt{{left(2*2*10^340/36/15right)}^2+left(2*200*10^3right)^2}

$${ \left(100 \times 10 \right) }^{ -3 } \sqrt{ { \left( \frac{ 2 \cdot 2 \times 1 { 0 }^{ 3 } \frac{ 40 }{ 36 } }{ 15 } \right) }^{ 2 } + { \left(2 \cdot 200 \times { 10 }^{ 3 } \right) }^{ 2 } }$$

Ovrednoti

$$\frac{1}{2500}=0,0004$$

Koraki rešitve

Pomnožite 100 in 10, da dobite 1000.

$$1000^{-3}\sqrt{\left(\frac{2\times 2\times 1\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Izračunajte potenco 1000 števila -3, da dobite \frac{1}{1000000000}.

$$\frac{1}{1000000000}\sqrt{\left(\frac{2\times 2\times 1\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Pomnožite 2 in 2, da dobite 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 1\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Pomnožite 4 in 1, da dobite 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Izračunajte potenco 0 števila 3, da dobite 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 0\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Pomnožite 4 in 0, da dobite 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Zmanjšajte ulomek \frac{40}{36} na najmanjši imenovalec tako, da izpeljete in okrajšate 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{10}{9}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Pomnožite 0 in \frac{10}{9}, da dobite 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Vrednost nič, deljena s poljubno vrednostjo, ki ni nič, da vrednost nič.

$$\frac{1}{1000000000}\sqrt{0^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Izračunajte potenco 0 števila 2, da dobite 0.

$$\frac{1}{1000000000}\sqrt{0+\left(2\times 200\times 10^{3}\right)^{2}}$$

Pomnožite 2 in 200, da dobite 400.

$$\frac{1}{1000000000}\sqrt{0+\left(400\times 10^{3}\right)^{2}}$$

Izračunajte potenco 10 števila 3, da dobite 1000.

$$\frac{1}{1000000000}\sqrt{0+\left(400\times 1000\right)^{2}}$$

Pomnožite 400 in 1000, da dobite 400000.

$$\frac{1}{1000000000}\sqrt{0+400000^{2}}$$

Izračunajte potenco 400000 števila 2, da dobite 160000000000.

$$\frac{1}{1000000000}\sqrt{0+160000000000}$$

Seštejte 0 in 160000000000, da dobite 160000000000.

$$\frac{1}{1000000000}\sqrt{160000000000}$$

Izračunajte kvadratni koren števila 160000000000 in dobite 400000.

$$\frac{1}{1000000000}\times 400000$$

Pomnožite \frac{1}{1000000000} in 400000, da dobite \frac{1}{2500}.

$$\frac{1}{2500}$$

Faktoriziraj

$$\frac{1}{2 ^ {2} \cdot 5 ^ {4}} = 0,0004$$