Solve {l}{C=2^3*5^2*7}{D=2^4*5^5*13}{a=C}{b=D}{text{Solvefor}c,dtext{where}}{c=a}{d=b}

$$\left. \begin{array} { l } { C = 2 ^ {3} \cdot 5 ^ {2} \cdot 7 }\\ { D = 2 ^ {4} \cdot 5 ^ {5} \cdot 13 }\\ { a = C }\\ { b = D }\\ { \text{Solve for } c,d \text{ where} } \\ { c = a }\\ { d = b } \end{array} \right.$$

Solve for C, D, a, b, c, d

$$c=1400$$

$$d=650000$$

Solution Steps

Consider the first equation. Calculate 2 to the power of 3 and get 8.

$$C=8\times 5^{2}\times 7$$

Calculate 5 to the power of 2 and get 25.

$$C=8\times 25\times 7$$

Multiply 8 and 25 to get 200.

$$C=200\times 7$$

Multiply 200 and 7 to get 1400.

$$C=1400$$

Consider the second equation. Calculate 2 to the power of 4 and get 16.

$$D=16\times 5^{5}\times 13$$

Calculate 5 to the power of 5 and get 3125.

$$D=16\times 3125\times 13$$

Multiply 16 and 3125 to get 50000.

$$D=50000\times 13$$

Multiply 50000 and 13 to get 650000.

$$D=650000$$

Consider the third equation. Insert the known values of variables into the equation.

$$a=1400$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$b=650000$$

Consider the fifth equation. Insert the known values of variables into the equation.

$$c=1400$$

Consider the equation (6). Insert the known values of variables into the equation.

$$d=650000$$

The system is now solved.

$$C=1400 D=650000 a=1400 b=650000 c=1400 d=650000$$