Solve [2^{10}div(-2)^{6}]^3*[16^3div(-4)^5]^2=

$$[ 2 ^ { 10 } \div ( - 2 ) ^ { 6 } ] ^ { 3 } \cdot [ 16 ^ { 3 } \div ( - 4 ) ^ { 5 } ] ^ { 2 } =$$

Evaluate

$$65536$$

Solution Steps

Calculate 2 to the power of 10 and get 1024.

$$\left(\frac{1024}{\left(-2\right)^{6}}\right)^{3}\times \left(\frac{16^{3}}{\left(-4\right)^{5}}\right)^{2}$$

Calculate -2 to the power of 6 and get 64.

$$\left(\frac{1024}{64}\right)^{3}\times \left(\frac{16^{3}}{\left(-4\right)^{5}}\right)^{2}$$

Divide 1024 by 64 to get 16.

$$16^{3}\times \left(\frac{16^{3}}{\left(-4\right)^{5}}\right)^{2}$$

Calculate 16 to the power of 3 and get 4096.

$$4096\times \left(\frac{16^{3}}{\left(-4\right)^{5}}\right)^{2}$$

Calculate 16 to the power of 3 and get 4096.

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

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

$$4096\times \left(\frac{4096}{-1024}\right)^{2}$$

Divide 4096 by -1024 to get -4.

$$4096\left(-4\right)^{2}$$

Calculate -4 to the power of 2 and get 16.

$$4096\times 16$$

Multiply 4096 and 16 to get 65536.

$$65536$$

Factor

$$2^{16}$$