Solve {[(2^{3})^{5}:2^{11}-3^{2}-2^{2}]*3^9}:(3^4)^2+0^3

$$\{ [ ( 2 ^ { 3 } ) ^ { 5 } : 2 ^ { 11 } - 3 ^ { 2 } - 2 ^ { 2 } ] \times 3 ^ { 9 } \} : ( 3 ^ { 4 } ) ^ { 2 } + 0 ^ { 3 }$$

Evaluate

$$9$$

Solution Steps

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

$$\frac{\left(\frac{2^{15}}{2^{11}}-3^{2}-2^{2}\right)\times 3^{9}}{\left(3^{4}\right)^{2}}+0^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 15 to get 4.

$$\frac{\left(2^{4}-3^{2}-2^{2}\right)\times 3^{9}}{\left(3^{4}\right)^{2}}+0^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(2^{4}-3^{2}-2^{2}\right)\times 3^{9}}{3^{8}}+0^{3}$$

Cancel out 3^{8} in both numerator and denominator.

$$3\left(2^{4}-3^{2}-2^{2}\right)+0^{3}$$

Calculate 0 to the power of 3 and get 0.

$$3\left(2^{4}-3^{2}-2^{2}\right)+0$$

Anything plus zero gives itself.

$$3\left(2^{4}-3^{2}-2^{2}\right)$$

Calculate 2 to the power of 4 and get 16.

$$3\left(16-3^{2}-2^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$3\left(16-9-2^{2}\right)$$

Subtract 9 from 16 to get 7.

$$3\left(7-2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$3\left(7-4\right)$$

Subtract 4 from 7 to get 3.

$$3\times 3$$

Multiply 3 and 3 to get 9.

$$9$$

Factor

$$3^{2}$$