Solve 5.3*10^18*10^3*8.3*300/29*frac{4{3}pi*(6.4*10^6)^3}

$$\frac { 5.3 \times 10 ^ { 18 } \times 10 ^ { 3 } \times 8.3 \times 300 } { 29 \times \frac { 4 } { 3 } \pi \times ( 6.4 \times 10 ^ { 6 } ) ^ { 3 } }$$

Evaluate

$$\frac{618609375}{475136\pi }\approx 414.427615985$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 18 and 3 to get 21.

$$\frac{5.3\times 10^{21}\times 8.3\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Calculate 10 to the power of 21 and get 1000000000000000000000.

$$\frac{5.3\times 1000000000000000000000\times 8.3\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 5.3 and 1000000000000000000000 to get 5300000000000000000000.

$$\frac{5300000000000000000000\times 8.3\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 5300000000000000000000 and 8.3 to get 43990000000000000000000.

$$\frac{43990000000000000000000\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 43990000000000000000000 and 300 to get 13197000000000000000000000.

$$\frac{13197000000000000000000000}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 29 and \frac{4}{3} to get \frac{116}{3}.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times \left(6.4\times 1000000\right)^{3}}$$

Multiply 6.4 and 1000000 to get 6400000.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times 6400000^{3}}$$

Calculate 6400000 to the power of 3 and get 262144000000000000000.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times 262144000000000000000}$$

Multiply \frac{116}{3} and 262144000000000000000 to get \frac{30408704000000000000000}{3}.

$$\frac{13197000000000000000000000}{\frac{30408704000000000000000}{3}\pi }$$

Expand

$$\frac{618609375}{475136 \pi} = 414.42761598463574$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 18 and 3 to get 21.

$$\frac{5.3\times 10^{21}\times 8.3\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Calculate 10 to the power of 21 and get 1000000000000000000000.

$$\frac{5.3\times 1000000000000000000000\times 8.3\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 5.3 and 1000000000000000000000 to get 5300000000000000000000.

$$\frac{5300000000000000000000\times 8.3\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 5300000000000000000000 and 8.3 to get 43990000000000000000000.

$$\frac{43990000000000000000000\times 300}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 43990000000000000000000 and 300 to get 13197000000000000000000000.

$$\frac{13197000000000000000000000}{29\times \frac{4}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Multiply 29 and \frac{4}{3} to get \frac{116}{3}.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times \left(6.4\times 10^{6}\right)^{3}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times \left(6.4\times 1000000\right)^{3}}$$

Multiply 6.4 and 1000000 to get 6400000.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times 6400000^{3}}$$

Calculate 6400000 to the power of 3 and get 262144000000000000000.

$$\frac{13197000000000000000000000}{\frac{116}{3}\pi \times 262144000000000000000}$$

Multiply \frac{116}{3} and 262144000000000000000 to get \frac{30408704000000000000000}{3}.

$$\frac{13197000000000000000000000}{\frac{30408704000000000000000}{3}\pi }$$