Solve {[(2^{5}*2^{4})^{2}:(2^{5})^{3}]^{2}*(5^{12}:5^11):2^4}-(5*2^2-4^2)

$$\{ [ ( 2 ^ { 5 } \times 2 ^ { 4 } ) ^ { 2 } : ( 2 ^ { 5 } ) ^ { 3 } ] ^ { 2 } \times ( 5 ^ { 12 } : 5 ^ { 11 } ) : 2 ^ { 4 } \} - ( 5 \times 2 ^ { 2 } - 4 ^ { 2 } )$$

Evaluate

$$16$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{\left(\frac{\left(2^{9}\right)^{2}}{\left(2^{5}\right)^{3}}\right)^{2}\times \frac{5^{12}}{5^{11}}}{2^{4}}-\left(5\times 2^{2}-4^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{\left(\frac{2^{18}}{\left(2^{5}\right)^{3}}\right)^{2}\times \frac{5^{12}}{5^{11}}}{2^{4}}-\left(5\times 2^{2}-4^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\left(\frac{2^{18}}{2^{15}}\right)^{2}\times \frac{5^{12}}{5^{11}}}{2^{4}}-\left(5\times 2^{2}-4^{2}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 15 from 18 to get 3.

$$\frac{\left(2^{3}\right)^{2}\times \frac{5^{12}}{5^{11}}}{2^{4}}-\left(5\times 2^{2}-4^{2}\right)$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{6}\times \frac{5^{12}}{5^{11}}}{2^{4}}-\left(5\times 2^{2}-4^{2}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 12 to get 1.

$$\frac{2^{6}\times 5^{1}}{2^{4}}-\left(5\times 2^{2}-4^{2}\right)$$

Cancel out 2^{4} in both numerator and denominator.

$$2^{2}\times 5^{1}-\left(5\times 2^{2}-4^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$2^{2}\times 5^{1}-\left(5\times 4-4^{2}\right)$$

Multiply 5 and 4 to get 20.

$$2^{2}\times 5^{1}-\left(20-4^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$2^{2}\times 5^{1}-\left(20-16\right)$$

Subtract 16 from 20 to get 4.

$$2^{2}\times 5^{1}-4$$

Calculate 2 to the power of 2 and get 4.

$$4\times 5^{1}-4$$

Calculate 5 to the power of 1 and get 5.

$$4\times 5-4$$

Multiply 4 and 5 to get 20.

$$20-4$$

Subtract 4 from 20 to get 16.

$$16$$

Factor

$$2^{4}$$