Ratkaise (228*10^11)^3/(594*10^7)^2

$$\frac { ( 228 \times 10 ^ { 11 } ) ^ { 3 } } { ( 594 \times 10 ^ { 7 } ) ^ { 2 } }$$

Laske

$$\frac{1097440000000000000000000}{3267}\approx 3,359167432 \cdot 10^{20}$$

Ratkaisun vaiheet

Laske 10 potenssiin 11, jolloin ratkaisuksi tulee 100000000000.

$$\frac{\left(228\times 100000000000\right)^{3}}{\left(594\times 10^{7}\right)^{2}}$$

Kerro 228 ja 100000000000, niin saadaan 22800000000000.

$$\frac{22800000000000^{3}}{\left(594\times 10^{7}\right)^{2}}$$

Laske 22800000000000 potenssiin 3, jolloin ratkaisuksi tulee 11852352000000000000000000000000000000000.

$$\frac{11852352000000000000000000000000000000000}{\left(594\times 10^{7}\right)^{2}}$$

Laske 10 potenssiin 7, jolloin ratkaisuksi tulee 10000000.

$$\frac{11852352000000000000000000000000000000000}{\left(594\times 10000000\right)^{2}}$$

Kerro 594 ja 10000000, niin saadaan 5940000000.

$$\frac{11852352000000000000000000000000000000000}{5940000000^{2}}$$

Laske 5940000000 potenssiin 2, jolloin ratkaisuksi tulee 35283600000000000000.

$$\frac{11852352000000000000000000000000000000000}{35283600000000000000}$$

Supista murtoluku \frac{11852352000000000000000000000000000000000}{35283600000000000000} luvulla 10800000000000000.

$$\frac{1097440000000000000000000}{3267}$$

Jaa tekijöihin

$$\frac{2 ^ {23} \cdot 5 ^ {19} \cdot 19 ^ {3}}{3 ^ {3} \cdot 11 ^ {2}} = 3,3591674318947042 \times 10^{20}\frac{1353}{3267} = 3,3591674318947042 \times 10^{20}$$