Solve 32^9*32:8^10*4^2/(-2)^12

$$\frac { 32 ^ { 9 } \cdot 32 : 8 ^ { 10 } \cdot 4 ^ { 2 } } { ( - 2 ) ^ { 12 } }$$

Evaluate

$$4096$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{\frac{32^{10}}{8^{10}}\times 4^{2}}{\left(-2\right)^{12}}$$

Calculate 32 to the power of 10 and get 1125899906842624.

$$\frac{\frac{1125899906842624}{8^{10}}\times 4^{2}}{\left(-2\right)^{12}}$$

Calculate 8 to the power of 10 and get 1073741824.

$$\frac{\frac{1125899906842624}{1073741824}\times 4^{2}}{\left(-2\right)^{12}}$$

Divide 1125899906842624 by 1073741824 to get 1048576.

$$\frac{1048576\times 4^{2}}{\left(-2\right)^{12}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1048576\times 16}{\left(-2\right)^{12}}$$

Multiply 1048576 and 16 to get 16777216.

$$\frac{16777216}{\left(-2\right)^{12}}$$

Calculate -2 to the power of 12 and get 4096.

$$\frac{16777216}{4096}$$

Divide 16777216 by 4096 to get 4096.

$$4096$$

Factor

$$2^{12}$$