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

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

Baholash

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

Yechim qadamlari

1000 hosil qilish uchun 100 va 10 ni ko'paytirish.

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

-3 daraja ko‘rsatkichini 1000 ga hisoblang va \frac{1}{1000000000} ni qiymatni oling.

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

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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

4 hosil qilish uchun 4 va 1 ni ko'paytirish.

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

3 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

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

0 hosil qilish uchun 4 va 0 ni ko'paytirish.

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

\frac{40}{36} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

0 hosil qilish uchun 0 va \frac{10}{9} ni ko'paytirish.

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

Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

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

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

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

400 hosil qilish uchun 2 va 200 ni ko'paytirish.

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

3 daraja ko‘rsatkichini 10 ga hisoblang va 1000 ni qiymatni oling.

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

400000 hosil qilish uchun 400 va 1000 ni ko'paytirish.

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

2 daraja ko‘rsatkichini 400000 ga hisoblang va 160000000000 ni qiymatni oling.

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

160000000000 olish uchun 0 va 160000000000'ni qo'shing.

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

160000000000 ning kvadrat ildizini hisoblab, 400000 natijaga ega bo‘ling.

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

\frac{1}{2500} hosil qilish uchun \frac{1}{1000000000} va 400000 ni ko'paytirish.

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

Omil

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