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

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

Evaluate

$$9$$

Solution Steps

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

$$\frac{\left(\frac{2^{15}}{2^{11}}-3^{2}-2^{2}\right)^{5}\times 3^{9}}{\left(3^{4}\right)^{3}}+0$$

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

$$\frac{\left(2^{4}-3^{2}-2^{2}\right)^{5}\times 3^{9}}{\left(3^{4}\right)^{3}}+0$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\left(2^{4}-3^{2}-2^{2}\right)^{5}\times 3^{9}}{3^{12}}+0$$

Cancel out 3^{9} in both numerator and denominator.

$$\frac{\left(2^{4}-3^{2}-2^{2}\right)^{5}}{3^{3}}+0$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(16-3^{2}-2^{2}\right)^{5}}{3^{3}}+0$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(16-9-2^{2}\right)^{5}}{3^{3}}+0$$

Subtract 9 from 16 to get 7.

$$\frac{\left(7-2^{2}\right)^{5}}{3^{3}}+0$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(7-4\right)^{5}}{3^{3}}+0$$

Subtract 4 from 7 to get 3.

$$\frac{3^{5}}{3^{3}}+0$$

Calculate 3 to the power of 5 and get 243.

$$\frac{243}{3^{3}}+0$$

Calculate 3 to the power of 3 and get 27.

$$\frac{243}{27}+0$$

Divide 243 by 27 to get 9.

$$9+0$$

Add 9 and 0 to get 9.

$$9$$

Factor

$$3^{2}$$