Solve (-2)^{3}*(-2)^{2}:(+2)^{4}-5^{2}:(-1)^5+(3^2)^5:(-3)^8=

$$( - 2 ) ^ { 3 } \cdot ( - 2 ) ^ { 2 } : ( + 2 ) ^ { 4 } - 5 ^ { 2 } : ( - 1 ) ^ { 5 } + ( 3 ^ { 2 } ) ^ { 5 } : ( - 3 ) ^ { 8 } =$$

Evaluate

$$32$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\left(-2\right)^{5}}{2^{4}}-\frac{5^{2}}{\left(-1\right)^{5}}+\frac{\left(3^{2}\right)^{5}}{\left(-3\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{\left(-2\right)^{5}}{2^{4}}-\frac{5^{2}}{\left(-1\right)^{5}}+\frac{3^{10}}{\left(-3\right)^{8}}$$

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

$$\frac{-32}{2^{4}}-\frac{5^{2}}{\left(-1\right)^{5}}+\frac{3^{10}}{\left(-3\right)^{8}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{-32}{16}-\frac{5^{2}}{\left(-1\right)^{5}}+\frac{3^{10}}{\left(-3\right)^{8}}$$

Divide -32 by 16 to get -2.

$$-2-\frac{5^{2}}{\left(-1\right)^{5}}+\frac{3^{10}}{\left(-3\right)^{8}}$$

Calculate 5 to the power of 2 and get 25.

$$-2-\frac{25}{\left(-1\right)^{5}}+\frac{3^{10}}{\left(-3\right)^{8}}$$

Calculate -1 to the power of 5 and get -1.

$$-2-\frac{25}{-1}+\frac{3^{10}}{\left(-3\right)^{8}}$$

Fraction \frac{25}{-1} can be rewritten as -25 by extracting the negative sign.

$$-2-\left(-25\right)+\frac{3^{10}}{\left(-3\right)^{8}}$$

The opposite of -25 is 25.

$$-2+25+\frac{3^{10}}{\left(-3\right)^{8}}$$

Add -2 and 25 to get 23.

$$23+\frac{3^{10}}{\left(-3\right)^{8}}$$

Calculate 3 to the power of 10 and get 59049.

$$23+\frac{59049}{\left(-3\right)^{8}}$$

Calculate -3 to the power of 8 and get 6561.

$$23+\frac{59049}{6561}$$

Divide 59049 by 6561 to get 9.

$$23+9$$

Add 23 and 9 to get 32.

$$32$$

Factor

$$2^{5}$$