Solve sqrt{1/3^-2+1/2^-4}

$$\sqrt{ \frac{ 1 }{ { 3 }^{ -2 } } + \frac{ 1 }{ { 2 }^{ -4 } } }$$

Evaluate

$$5$$

Solution Steps

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\sqrt{\frac{1}{\frac{1}{9}}+\frac{1}{2^{-4}}}$$

Divide 1 by \frac{1}{9} by multiplying 1 by the reciprocal of \frac{1}{9}.

$$\sqrt{1\times 9+\frac{1}{2^{-4}}}$$

Multiply 1 and 9 to get 9.

$$\sqrt{9+\frac{1}{2^{-4}}}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\sqrt{9+\frac{1}{\frac{1}{16}}}$$

Divide 1 by \frac{1}{16} by multiplying 1 by the reciprocal of \frac{1}{16}.

$$\sqrt{9+1\times 16}$$

Multiply 1 and 16 to get 16.

$$\sqrt{9+16}$$

Add 9 and 16 to get 25.

$$\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$5$$

Factor

$$5$$