Solve [frac{(2^{2})^{2}+3^2}{2^2*3^2}]^-frac{1{2}}

$$[ \frac { ( 2 ^ { 2 } ) ^ { 2 } + 3 ^ { 2 } } { 2 ^ { 2 } \cdot 3 ^ { 2 } } ] ^ { - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

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

$$\left(\frac{2^{4}+3^{2}}{2^{2}\times 3^{2}}\right)^{-\frac{1}{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\left(\frac{16+3^{2}}{2^{2}\times 3^{2}}\right)^{-\frac{1}{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{16+9}{2^{2}\times 3^{2}}\right)^{-\frac{1}{2}}$$

Add 16 and 9 to get 25.

$$\left(\frac{25}{2^{2}\times 3^{2}}\right)^{-\frac{1}{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{25}{4\times 3^{2}}\right)^{-\frac{1}{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{25}{4\times 9}\right)^{-\frac{1}{2}}$$

Multiply 4 and 9 to get 36.

$$\left(\frac{25}{36}\right)^{-\frac{1}{2}}$$

Calculate \frac{25}{36} to the power of -\frac{1}{2} and get \frac{6}{5}.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$