Solve A=(2^{8}*2^{5}*2^{7})^{2}:4^{15}+(4^{16}:2^{32}-2^0)*(2^4*3^4-6^4)

$$A = ( 2 ^ { 8 } \cdot 2 ^ { 5 } \cdot 2 ^ { 7 } ) ^ { 2 } : 4 ^ { 15 } + ( 4 ^ { 16 } : 2 ^ { 32 } - 2 ^ { 0 } ) \cdot ( 2 ^ { 4 } \cdot 3 ^ { 4 } - 6 ^ { 4 } )$$

Solve for A

$$A=1024$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$A=\frac{\left(2^{13}\times 2^{7}\right)^{2}}{4^{15}}+\left(\frac{4^{16}}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

To multiply powers of the same base, add their exponents. Add 13 and 7 to get 20.

$$A=\frac{\left(2^{20}\right)^{2}}{4^{15}}+\left(\frac{4^{16}}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

To raise a power to another power, multiply the exponents. Multiply 20 and 2 to get 40.

$$A=\frac{2^{40}}{4^{15}}+\left(\frac{4^{16}}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Calculate 2 to the power of 40 and get 1099511627776.

$$A=\frac{1099511627776}{4^{15}}+\left(\frac{4^{16}}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Calculate 4 to the power of 15 and get 1073741824.

$$A=\frac{1099511627776}{1073741824}+\left(\frac{4^{16}}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Divide 1099511627776 by 1073741824 to get 1024.

$$A=1024+\left(\frac{4^{16}}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Calculate 4 to the power of 16 and get 4294967296.

$$A=1024+\left(\frac{4294967296}{2^{32}}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Calculate 2 to the power of 32 and get 4294967296.

$$A=1024+\left(\frac{4294967296}{4294967296}-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Divide 4294967296 by 4294967296 to get 1.

$$A=1024+\left(1-2^{0}\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Calculate 2 to the power of 0 and get 1.

$$A=1024+\left(1-1\right)\left(2^{4}\times 3^{4}-6^{4}\right)$$

Subtract 1 from 1 to get 0.

$$A=1024+0\left(2^{4}\times 3^{4}-6^{4}\right)$$

Calculate 2 to the power of 4 and get 16.

$$A=1024+0\left(16\times 3^{4}-6^{4}\right)$$

Calculate 3 to the power of 4 and get 81.

$$A=1024+0\left(16\times 81-6^{4}\right)$$

Multiply 16 and 81 to get 1296.

$$A=1024+0\left(1296-6^{4}\right)$$

Calculate 6 to the power of 4 and get 1296.

$$A=1024+0\left(1296-1296\right)$$

Subtract 1296 from 1296 to get 0.

$$A=1024+0\times 0$$

Multiply 0 and 0 to get 0.

$$A=1024+0$$

Add 1024 and 0 to get 1024.

$$A=1024$$

Assign A

$$A≔1024$$