Solve (-5)^{6}*(-5)^{3}:(+5)^{7}+(-2^{2})^7:(-2)^10+(-3)^9:(-3)^4=

$$( - 5 ) ^ { 6 } \cdot ( - 5 ) ^ { 3 } : ( + 5 ) ^ { 7 } + ( - 2 ^ { 2 } ) ^ { 7 } : ( - 2 ) ^ { 10 } + ( - 3 ) ^ { 9 } : ( - 3 ) ^ { 4 } =$$

Evaluate

$$-284$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\left(-5\right)^{9}}{5^{7}}+\frac{\left(-2^{2}\right)^{7}}{\left(-2\right)^{10}}+\frac{\left(-3\right)^{9}}{\left(-3\right)^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 9 to get 5.

$$\frac{\left(-5\right)^{9}}{5^{7}}+\frac{\left(-2^{2}\right)^{7}}{\left(-2\right)^{10}}+\left(-3\right)^{5}$$

Calculate -5 to the power of 9 and get -1953125.

$$\frac{-1953125}{5^{7}}+\frac{\left(-2^{2}\right)^{7}}{\left(-2\right)^{10}}+\left(-3\right)^{5}$$

Calculate 5 to the power of 7 and get 78125.

$$\frac{-1953125}{78125}+\frac{\left(-2^{2}\right)^{7}}{\left(-2\right)^{10}}+\left(-3\right)^{5}$$

Divide -1953125 by 78125 to get -25.

$$-25+\frac{\left(-2^{2}\right)^{7}}{\left(-2\right)^{10}}+\left(-3\right)^{5}$$

Calculate 2 to the power of 2 and get 4.

$$-25+\frac{\left(-4\right)^{7}}{\left(-2\right)^{10}}+\left(-3\right)^{5}$$

Calculate -4 to the power of 7 and get -16384.

$$-25+\frac{-16384}{\left(-2\right)^{10}}+\left(-3\right)^{5}$$

Calculate -2 to the power of 10 and get 1024.

$$-25+\frac{-16384}{1024}+\left(-3\right)^{5}$$

Divide -16384 by 1024 to get -16.

$$-25-16+\left(-3\right)^{5}$$

Subtract 16 from -25 to get -41.

$$-41+\left(-3\right)^{5}$$

Calculate -3 to the power of 5 and get -243.

$$-41-243$$

Subtract 243 from -41 to get -284.

$$-284$$

Factor

$$-284$$