Solve x={[(-2)^{7}*(-2)^{31}]^2:2^70-(-2)^3}:(-3)^2

$$x = \{ [ ( - 2 ) ^ { 7 } \cdot ( - 2 ) ^ { 31 } ] ^ { 2 } : 2 ^ { 70 } - ( - 2 ) ^ { 3 } \} : ( - 3 ) ^ { 2 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 7 and 31 to get 38.

$$x=\frac{\frac{\left(\left(-2\right)^{38}\right)^{2}}{2^{70}}-\left(-2\right)^{3}}{\left(-3\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 38 and 2 to get 76.

$$x=\frac{\frac{\left(-2\right)^{76}}{2^{70}}-\left(-2\right)^{3}}{\left(-3\right)^{2}}$$

Calculate -2 to the power of 76 and get 75557863725914323419136.

$$x=\frac{\frac{75557863725914323419136}{2^{70}}-\left(-2\right)^{3}}{\left(-3\right)^{2}}$$

Calculate 2 to the power of 70 and get 1180591620717411303424.

$$x=\frac{\frac{75557863725914323419136}{1180591620717411303424}-\left(-2\right)^{3}}{\left(-3\right)^{2}}$$

Divide 75557863725914323419136 by 1180591620717411303424 to get 64.

$$x=\frac{64-\left(-2\right)^{3}}{\left(-3\right)^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$x=\frac{64-\left(-8\right)}{\left(-3\right)^{2}}$$

The opposite of -8 is 8.

$$x=\frac{64+8}{\left(-3\right)^{2}}$$

Add 64 and 8 to get 72.

$$x=\frac{72}{\left(-3\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$x=\frac{72}{9}$$

Divide 72 by 9 to get 8.

$$x=8$$

Assign x

$$x≔8$$