Solve [(2^{2})^{2}-2^{4}]:(2^{3})^{2}+(3^{3})^{2}:[(3^{4})^3:(3^5)^2]^2=

$$[ ( 2 ^ { 2 } ) ^ { 2 } - 2 ^ { 4 } ] : ( 2 ^ { 3 } ) ^ { 2 } + ( 3 ^ { 3 } ) ^ { 2 } : [ ( 3 ^ { 4 } ) ^ { 3 } : ( 3 ^ { 5 } ) ^ { 2 } ] ^ { 2 } =$$

Evaluate

$$9$$

Solution Steps

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

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

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

$$\frac{2^{4}-2^{4}}{2^{6}}+\frac{\left(3^{3}\right)^{2}}{\left(\frac{\left(3^{4}\right)^{3}}{\left(3^{5}\right)^{2}}\right)^{2}}$$

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

$$\frac{2^{4}-2^{4}}{2^{6}}+\frac{3^{6}}{\left(\frac{\left(3^{4}\right)^{3}}{\left(3^{5}\right)^{2}}\right)^{2}}$$

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

$$\frac{2^{4}-2^{4}}{2^{6}}+\frac{3^{6}}{\left(\frac{3^{12}}{\left(3^{5}\right)^{2}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{2^{4}-2^{4}}{2^{6}}+\frac{3^{6}}{\left(\frac{3^{12}}{3^{10}}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 12 to get 2.

$$\frac{2^{4}-2^{4}}{2^{6}}+\frac{3^{6}}{\left(3^{2}\right)^{2}}$$

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

$$\frac{2^{4}-2^{4}}{2^{6}}+\frac{3^{6}}{3^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$\frac{2^{4}-2^{4}}{2^{6}}+3^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16-2^{4}}{2^{6}}+3^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16-16}{2^{6}}+3^{2}$$

Subtract 16 from 16 to get 0.

$$\frac{0}{2^{6}}+3^{2}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{0}{64}+3^{2}$$

Zero divided by any non-zero number gives zero.

$$0+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$0+9$$

Add 0 and 9 to get 9.

$$9$$

Factor

$$3^{2}$$