Solve (1.96*10^4)^3/(4.8*10^4)^3

$$\frac { ( 1.96 \times 10 ^ { 4 } ) ^ { 3 } } { ( 4.8 \times 10 ^ { 4 } ) ^ { 3 } }$$

Evaluate

$$\frac{117649}{1728000}\approx 0.068083912$$

Solution Steps

Calculate 10 to the power of 4 and get 10000.

$$\frac{\left(1.96\times 10000\right)^{3}}{\left(4.8\times 10^{4}\right)^{3}}$$

Multiply 1.96 and 10000 to get 19600.

$$\frac{19600^{3}}{\left(4.8\times 10^{4}\right)^{3}}$$

Calculate 19600 to the power of 3 and get 7529536000000.

$$\frac{7529536000000}{\left(4.8\times 10^{4}\right)^{3}}$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{7529536000000}{\left(4.8\times 10000\right)^{3}}$$

Multiply 4.8 and 10000 to get 48000.

$$\frac{7529536000000}{48000^{3}}$$

Calculate 48000 to the power of 3 and get 110592000000000.

$$\frac{7529536000000}{110592000000000}$$

Reduce the fraction \frac{7529536000000}{110592000000000} to lowest terms by extracting and canceling out 64000000.

$$\frac{117649}{1728000}$$

Factor

$$\frac{7 ^ {6}}{2 ^ {9} \cdot 3 ^ {3} \cdot 5 ^ {3}} = 0.06808391203703704$$