Решете 347*10^22div667*10^-11div6*10^24*15*10^11*15*{10}^11

$$347 \times { 10 }^{ 22 } \div 667 \times { 10 }^{ -11 } \div 6 \times { 10 }^{ 24 } \times 15 \times { 10 }^{ 11 } \times 15 \times { 10 }^{ 11 }$$

Изчисляване

$$\frac{13012500000000000000000000000000000000000000000000000000000000}{667}\approx 1,95089955 \cdot 10^{58}$$

Стъпки на решението

За да умножите степени с една и съща основа, съберете техните експоненти. Съберете 24 и 11, за да получите 35.

$$\frac{\frac{347\times 10^{22}}{667}\times 10^{-11}}{6}\times 10^{35}\times 15\times 15\times 10^{11}$$

За да умножите степени с една и съща основа, съберете техните експоненти. Съберете 35 и 11, за да получите 46.

$$\frac{\frac{347\times 10^{22}}{667}\times 10^{-11}}{6}\times 10^{46}\times 15\times 15$$

Изчислявате 22 на степен 10 и получавате 10000000000000000000000.

$$\frac{\frac{347\times 10000000000000000000000}{667}\times 10^{-11}}{6}\times 10^{46}\times 15\times 15$$

Умножете 347 по 10000000000000000000000, за да получите 3470000000000000000000000.

$$\frac{\frac{3470000000000000000000000}{667}\times 10^{-11}}{6}\times 10^{46}\times 15\times 15$$

Изчислявате -11 на степен 10 и получавате \frac{1}{100000000000}.

$$\frac{\frac{3470000000000000000000000}{667}\times \frac{1}{100000000000}}{6}\times 10^{46}\times 15\times 15$$

Умножете \frac{3470000000000000000000000}{667} по \frac{1}{100000000000}, за да получите \frac{34700000000000}{667}.

$$\frac{\frac{34700000000000}{667}}{6}\times 10^{46}\times 15\times 15$$

Изразете \frac{\frac{34700000000000}{667}}{6} като една дроб.

$$\frac{34700000000000}{667\times 6}\times 10^{46}\times 15\times 15$$

Умножете 667 по 6, за да получите 4002.

$$\frac{34700000000000}{4002}\times 10^{46}\times 15\times 15$$

Намаляване на дробта \frac{34700000000000}{4002} до най-малките членове чрез извличане на корен и съкращаване на 2.

$$\frac{17350000000000}{2001}\times 10^{46}\times 15\times 15$$

Изчислявате 46 на степен 10 и получавате 10000000000000000000000000000000000000000000000.

$$\frac{17350000000000}{2001}\times 10000000000000000000000000000000000000000000000\times 15\times 15$$

Умножете \frac{17350000000000}{2001} по 10000000000000000000000000000000000000000000000, за да получите \frac{173500000000000000000000000000000000000000000000000000000000}{2001}.

$$\frac{173500000000000000000000000000000000000000000000000000000000}{2001}\times 15\times 15$$

Умножете \frac{173500000000000000000000000000000000000000000000000000000000}{2001} по 15, за да получите \frac{867500000000000000000000000000000000000000000000000000000000}{667}.

$$\frac{867500000000000000000000000000000000000000000000000000000000}{667}\times 15$$

Умножете \frac{867500000000000000000000000000000000000000000000000000000000}{667} по 15, за да получите \frac{13012500000000000000000000000000000000000000000000000000000000}{667}.

$$\frac{13012500000000000000000000000000000000000000000000000000000000}{667}$$

Разлагане на множители

$$\frac{2 ^ {56} \cdot 3 \cdot 5 ^ {59} \cdot 347}{23 \cdot 29} = 1,950899550224888 \times 10^{58}\frac{535}{667} = 1,950899550224888 \times 10^{58}$$