Solve sqrt{(frac{(10^-(frac{2{3})})^-6}{(5^-3/5)^-4})+0!}

$$\sqrt { ( \frac { ( 10 ^ { - ( \frac { 2 } { 3 } ) } ) ^ { - 6 } } { ( \frac { 5 ^ { - 3 } } { 5 } ) ^ { - 4 } } ) + 0 ! }$$

Evaluate

$$\frac{\sqrt{244140641}}{15625}\approx 1.000000033$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{3} and -6 to get 4.

$$\sqrt{\frac{10^{4}}{\left(\frac{5^{-3}}{5}\right)^{-4}}+0!}$$

Rewrite 5 as 5^{-3}\times 5^{4}. Cancel out 5^{-3} in both numerator and denominator.

$$\sqrt{\frac{10^{4}}{\left(\frac{1}{5^{4}}\right)^{-4}}+0!}$$

Calculate 10 to the power of 4 and get 10000.

$$\sqrt{\frac{10000}{\left(\frac{1}{5^{4}}\right)^{-4}}+0!}$$

Calculate 5 to the power of 4 and get 625.

$$\sqrt{\frac{10000}{\left(\frac{1}{625}\right)^{-4}}+0!}$$

Calculate \frac{1}{625} to the power of -4 and get 152587890625.

$$\sqrt{\frac{10000}{152587890625}+0!}$$

Reduce the fraction \frac{10000}{152587890625} to lowest terms by extracting and canceling out 625.

$$\sqrt{\frac{16}{244140625}+0!}$$

The factorial of 0 is 1.

$$\sqrt{\frac{16}{244140625}+1}$$

Add \frac{16}{244140625} and 1 to get \frac{244140641}{244140625}.

$$\sqrt{\frac{244140641}{244140625}}$$

Rewrite the square root of the division \sqrt{\frac{244140641}{244140625}} as the division of square roots \frac{\sqrt{244140641}}{\sqrt{244140625}}.

$$\frac{\sqrt{244140641}}{\sqrt{244140625}}$$

Calculate the square root of 244140625 and get 15625.

$$\frac{\sqrt{244140641}}{15625}$$