Solve (-3)^{15}:(+3)^{13}-(-2)^{240}:(-2)^{235}+(-5^6)^3:(+5^8)^2=

$$( - 3 ) ^ { 15 } : ( + 3 ) ^ { 13 } - ( - 2 ) ^ { 240 } : ( - 2 ) ^ { 235 } + ( - 5 ^ { 6 } ) ^ { 3 } : ( + 5 ^ { 8 } ) ^ { 2 } =$$

Evaluate

$$-2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 235 from 240 to get 5.

$$\frac{\left(-3\right)^{15}}{3^{13}}-\left(-2\right)^{5}+\frac{\left(-5^{6}\right)^{3}}{\left(5^{8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\left(-3\right)^{15}}{3^{13}}-\left(-2\right)^{5}+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

Calculate -3 to the power of 15 and get -14348907.

$$\frac{-14348907}{3^{13}}-\left(-2\right)^{5}+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

Calculate 3 to the power of 13 and get 1594323.

$$\frac{-14348907}{1594323}-\left(-2\right)^{5}+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

Divide -14348907 by 1594323 to get -9.

$$-9-\left(-2\right)^{5}+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

Calculate -2 to the power of 5 and get -32.

$$-9-\left(-32\right)+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

The opposite of -32 is 32.

$$-9+32+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

Add -9 and 32 to get 23.

$$23+\frac{\left(-5^{6}\right)^{3}}{5^{16}}$$

Calculate 5 to the power of 6 and get 15625.

$$23+\frac{\left(-15625\right)^{3}}{5^{16}}$$

Calculate -15625 to the power of 3 and get -3814697265625.

$$23+\frac{-3814697265625}{5^{16}}$$

Calculate 5 to the power of 16 and get 152587890625.

$$23+\frac{-3814697265625}{152587890625}$$

Divide -3814697265625 by 152587890625 to get -25.

$$23-25$$

Subtract 25 from 23 to get -2.

$$-2$$

Factor

$$-2$$