Solve {l}{A=frac{2^{13}*5^{7}}{2^{4}*5^{9}}=}{B=frac{3^{8}*11^{2}}{3^{9}*11^3}=..}{C=9^2*17^3/17*3^5*7=}

$$\left. \begin{array} { l } { A = \frac { 2 ^ { 13 } \times 5 ^ { 7 } } { 2 ^ { 4 } \times 5 ^ { 9 } } = } \\ { B = \frac { 3 ^ { 8 } \times 11 ^ { 2 } } { 3 ^ { 9 } \times 11 ^ { 3 } } = . . } \\ { C = \frac { 9 ^ { 2 } \times 17 ^ { 3 } } { 17 \times 3 ^ { 5 } \times 7 } = } \end{array} \right.$$

Solve for A, B

$$A = \frac{512}{25} = 20\frac{12}{25} = 20.48$$

$$B=\frac{1}{33}\approx 0.03030303$$

Solution Steps

Consider the first equation. Cancel out 2^{4}\times 5^{7} in both numerator and denominator.

$$A=\frac{2^{9}}{5^{2}}$$

Calculate 2 to the power of 9 and get 512.

$$A=\frac{512}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$A=\frac{512}{25}$$

Consider the second equation. Cancel out 3^{8}\times 11^{2} in both numerator and denominator.

$$B=\frac{1}{3\times 11}$$

Multiply 3 and 11 to get 33.

$$B=\frac{1}{33}$$

The system is now solved.

$$A=\frac{512}{25} B=\frac{1}{33}$$