Solve {[(-2)^{5}*(-2)*(-2)^{0}]^3:[(-2)^4*(-2)^3]}:(-2)^10

$$\{ [ ( - 2 ) ^ { 5 } \cdot ( - 2 ) \cdot ( - 2 ) ^ { 0 } ] ^ { 3 } : [ ( - 2 ) ^ { 4 } \cdot ( - 2 ) ^ { 3 } ] \} : ( - 2 ) ^ { 10 }$$

Evaluate

$$-2$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\frac{\left(\left(-2\right)^{6}\left(-2\right)^{0}\right)^{3}}{\left(-2\right)^{4}\left(-2\right)^{3}}}{\left(-2\right)^{10}}$$

To multiply powers of the same base, add their exponents. Add 6 and 0 to get 6.

$$\frac{\frac{\left(\left(-2\right)^{6}\right)^{3}}{\left(-2\right)^{4}\left(-2\right)^{3}}}{\left(-2\right)^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{\frac{\left(-2\right)^{18}}{\left(-2\right)^{4}\left(-2\right)^{3}}}{\left(-2\right)^{10}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\frac{\left(-2\right)^{18}}{\left(-2\right)^{7}}}{\left(-2\right)^{10}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 18 to get 11.

$$\frac{\left(-2\right)^{11}}{\left(-2\right)^{10}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 11 to get 1.

$$\left(-2\right)^{1}$$

Calculate -2 to the power of 1 and get -2.

$$-2$$

Factor

$$-2$$