Solve {(-2)^{20}:[(-2)^3]^6-7}^16:(-27)^5

$$\{ ( - 2 ) ^ { 20 } : [ ( - 2 ) ^ { 3 } ] ^ { 6 } - 7 \} ^ { 16 } : ( - 27 ) ^ { 5 }$$

Evaluate

$$-3$$

Solution Steps

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

$$\frac{\left(\frac{\left(-2\right)^{20}}{\left(-2\right)^{18}}-7\right)^{16}}{\left(-27\right)^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 18 from 20 to get 2.

$$\frac{\left(\left(-2\right)^{2}-7\right)^{16}}{\left(-27\right)^{5}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{\left(4-7\right)^{16}}{\left(-27\right)^{5}}$$

Subtract 7 from 4 to get -3.

$$\frac{\left(-3\right)^{16}}{\left(-27\right)^{5}}$$

Calculate -3 to the power of 16 and get 43046721.

$$\frac{43046721}{\left(-27\right)^{5}}$$

Calculate -27 to the power of 5 and get -14348907.

$$\frac{43046721}{-14348907}$$

Divide 43046721 by -14348907 to get -3.

$$-3$$

Factor

$$-3$$