Solve 5^-5left(.5right)^6-{left({left(sqrt{5}right)}^5right)}^frac{2{5}}

$${ 5 }^{ -5 } { \left(.5 \right) }^{ 6 } - { \left( { \left( \sqrt{ 5 } \right) }^{ 5 } \right) }^{ \frac{ 2 }{ 5 } }$$

Evaluate

$$-4.999995$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and \frac{2}{5} to get 2.

$$5^{-5}\times 0.5^{6}-\left(\sqrt{5}\right)^{2}$$

Calculate 5 to the power of -5 and get \frac{1}{3125}.

$$\frac{1}{3125}\times 0.5^{6}-\left(\sqrt{5}\right)^{2}$$

Calculate 0.5 to the power of 6 and get 0.015625.

$$\frac{1}{3125}\times 0.015625-\left(\sqrt{5}\right)^{2}$$

Multiply \frac{1}{3125} and 0.015625 to get \frac{1}{200000}.

$$\frac{1}{200000}-\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$\frac{1}{200000}-5$$

Subtract 5 from \frac{1}{200000} to get -\frac{999999}{200000}.

$$-\frac{999999}{200000}$$

Factor

$$-4.999995$$