Solve G1.99*10^30/4.59*10^10

$$G \frac { 1.99 \times 10 ^ { 30 } } { 4.59 \times 10 ^ { 10 } }$$

Evaluate

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

Solution Steps

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

$$G\times \frac{1.99\times 10^{20}}{4.59}$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$G\times \frac{1.99\times 100000000000000000000}{4.59}$$

Multiply 1.99 and 100000000000000000000 to get 199000000000000000000.

$$G\times \frac{199000000000000000000}{4.59}$$

Expand \frac{199000000000000000000}{4.59} by multiplying both numerator and the denominator by 100.

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

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.

$$\frac{\mathrm{d}}{\mathrm{d}G}(G\times \frac{1.99\times 10^{20}}{4.59})$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G}(G\times \frac{1.99\times 100000000000000000000}{4.59})$$

Multiply 1.99 and 100000000000000000000 to get 199000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G}(G\times \frac{199000000000000000000}{4.59})$$

Expand \frac{199000000000000000000}{4.59} by multiplying both numerator and the denominator by 100.

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

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.

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