Solve {l}{A=4^5*7^3}{B=7^2*4^6}{a=A*B}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { A = 4 ^ {5} \cdot 7 ^ {3} }\\ { B = 7 ^ {2} \cdot 4 ^ {6} }\\ { a = A \cdot B }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for A, B, a, b

$$b=70493667328$$

Solution Steps

Consider the first equation. Calculate 4 to the power of 5 and get 1024.

$$A=1024\times 7^{3}$$

Calculate 7 to the power of 3 and get 343.

$$A=1024\times 343$$

Multiply 1024 and 343 to get 351232.

$$A=351232$$

Consider the second equation. Calculate 7 to the power of 2 and get 49.

$$B=49\times 4^{6}$$

Calculate 4 to the power of 6 and get 4096.

$$B=49\times 4096$$

Multiply 49 and 4096 to get 200704.

$$B=200704$$

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

$$a=351232\times 200704$$

Multiply 351232 and 200704 to get 70493667328.

$$a=70493667328$$

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

$$b=70493667328$$

The system is now solved.

$$A=351232 B=200704 a=70493667328 b=70493667328$$