Solve sqrt{sqrt{sqrt{(8^6-2)^(-4)}}}

$$\sqrt { \sqrt { \sqrt { ( 8 ^ { 6 - 2 } ) ^ { ( - 4 ) } } } }$$

Evaluate

$$\frac{1}{64}=0.015625$$

Solution Steps

Subtract 2 from 6 to get 4.

$$\sqrt{\sqrt{\sqrt{\left(8^{4}\right)^{-4}}}}$$

Calculate 8 to the power of 4 and get 4096.

$$\sqrt{\sqrt{\sqrt{4096^{-4}}}}$$

Calculate 4096 to the power of -4 and get \frac{1}{281474976710656}.

$$\sqrt{\sqrt{\sqrt{\frac{1}{281474976710656}}}}$$

Rewrite the square root of the division \frac{1}{281474976710656} as the division of square roots \frac{\sqrt{1}}{\sqrt{281474976710656}}. Take the square root of both numerator and denominator.

$$\sqrt{\sqrt{\frac{1}{16777216}}}$$

Rewrite the square root of the division \frac{1}{16777216} as the division of square roots \frac{\sqrt{1}}{\sqrt{16777216}}. Take the square root of both numerator and denominator.

$$\sqrt{\frac{1}{4096}}$$

Rewrite the square root of the division \frac{1}{4096} as the division of square roots \frac{\sqrt{1}}{\sqrt{4096}}. Take the square root of both numerator and denominator.

$$\frac{1}{64}$$

Factor

$$\frac{1}{2 ^ {6}} = 0.015625$$