Solve [2^{12}*(-4)^{5}*(-8)^2]^2:(4^3)^9

$$[ 2 ^ { 12 } \cdot ( - 4 ) ^ { 5 } \cdot ( - 8 ) ^ { 2 } ] ^ { 2 } : ( 4 ^ { 3 } ) ^ { 9 }$$

Evaluate

$$4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\frac{\left(2^{12}\left(-4\right)^{5}\left(-8\right)^{2}\right)^{2}}{4^{27}}$$

Calculate 2 to the power of 12 and get 4096.

$$\frac{\left(4096\left(-4\right)^{5}\left(-8\right)^{2}\right)^{2}}{4^{27}}$$

Calculate -4 to the power of 5 and get -1024.

$$\frac{\left(4096\left(-1024\right)\left(-8\right)^{2}\right)^{2}}{4^{27}}$$

Multiply 4096 and -1024 to get -4194304.

$$\frac{\left(-4194304\left(-8\right)^{2}\right)^{2}}{4^{27}}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{\left(-4194304\times 64\right)^{2}}{4^{27}}$$

Multiply -4194304 and 64 to get -268435456.

$$\frac{\left(-268435456\right)^{2}}{4^{27}}$$

Calculate -268435456 to the power of 2 and get 72057594037927936.

$$\frac{72057594037927936}{4^{27}}$$

Calculate 4 to the power of 27 and get 18014398509481984.

$$\frac{72057594037927936}{18014398509481984}$$

Divide 72057594037927936 by 18014398509481984 to get 4.

$$4$$

Factor

$$2^{2}$$