Solve G199*10^30/459*10^10

$$G \frac { 199 \times 10 ^ { 30 } } { 459 \times 10 ^ { 10 } }$$

Evaluate

$$\frac{19900000000000000000000G}{459}$$

Solution Steps

Cancel out 10^{10} in both numerator and denominator.

$$G\times \frac{199\times 10^{20}}{459}$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$G\times \frac{199\times 100000000000000000000}{459}$$

Multiply 199 and 100000000000000000000 to get 19900000000000000000000.

$$G\times \frac{19900000000000000000000}{459}$$

Differentiate w.r.t. G

$$\frac{19900000000000000000000}{459} = 4.335511982570806 \times 10^{19}\frac{302}{459} = 4.335511982570806 \times 10^{19}$$

Steps Using Definition of a Derivative

Cancel out 10^{10} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}G}(G\times \frac{199\times 10^{20}}{459})$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G}(G\times \frac{199\times 100000000000000000000}{459})$$

Multiply 199 and 100000000000000000000 to get 19900000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G}(G\times \frac{19900000000000000000000}{459})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{19900000000000000000000}{459}G^{1-1}$$

Subtract 1 from 1.

$$\frac{19900000000000000000000}{459}G^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{19900000000000000000000}{459}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{19900000000000000000000}{459}$$