Solve (5^{13}*3^{13}):(15^{3})^{4}-(2^{3}*3^{1}):(2^{2}*3^2)*(2^4*3^2)^3

$$( 5 ^ { 13 } \cdot 3 ^ { 13 } ) : ( 15 ^ { 3 } ) ^ { 4 } - ( 2 ^ { 3 } \cdot 3 ^ { 1 } ) : ( 2 ^ { 2 } \cdot 3 ^ { 2 } ) \cdot ( 2 ^ { 4 } \cdot 3 ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-1990641$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{5^{13}\times 3^{13}}{15^{12}}-\frac{2^{3}\times 3^{1}}{2^{2}\times 3^{2}}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Calculate 5 to the power of 13 and get 1220703125.

$$\frac{1220703125\times 3^{13}}{15^{12}}-\frac{2^{3}\times 3^{1}}{2^{2}\times 3^{2}}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Calculate 3 to the power of 13 and get 1594323.

$$\frac{1220703125\times 1594323}{15^{12}}-\frac{2^{3}\times 3^{1}}{2^{2}\times 3^{2}}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Multiply 1220703125 and 1594323 to get 1946195068359375.

$$\frac{1946195068359375}{15^{12}}-\frac{2^{3}\times 3^{1}}{2^{2}\times 3^{2}}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Calculate 15 to the power of 12 and get 129746337890625.

$$\frac{1946195068359375}{129746337890625}-\frac{2^{3}\times 3^{1}}{2^{2}\times 3^{2}}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Divide 1946195068359375 by 129746337890625 to get 15.

$$15-\frac{2^{3}\times 3^{1}}{2^{2}\times 3^{2}}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Cancel out 3\times 2^{2} in both numerator and denominator.

$$15-\frac{2}{3}\times \left(2^{4}\times 3^{2}\right)^{3}$$

Calculate 2 to the power of 4 and get 16.

$$15-\frac{2}{3}\times \left(16\times 3^{2}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$15-\frac{2}{3}\times \left(16\times 9\right)^{3}$$

Multiply 16 and 9 to get 144.

$$15-\frac{2}{3}\times 144^{3}$$

Calculate 144 to the power of 3 and get 2985984.

$$15-\frac{2}{3}\times 2985984$$

Multiply \frac{2}{3} and 2985984 to get 1990656.

$$15-1990656$$

Subtract 1990656 from 15 to get -1990641.

$$-1990641$$

Factor

$$-1990641$$