Solve {(125)^-2*(16)^frac{-3{2}}}^-frac{1{6}}

$$\{ ( 125 ) ^ { - 2 } \times ( 16 ) ^ { \frac { - 3 } { 2 } } \} ^ { - \frac { 1 } { 6 } }$$

Evaluate

$$10$$

Solution Steps

Calculate 125 to the power of -2 and get \frac{1}{15625}.

$$\left(\frac{1}{15625}\times 16^{\frac{-3}{2}}\right)^{-\frac{1}{6}}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\left(\frac{1}{15625}\times 16^{-\frac{3}{2}}\right)^{-\frac{1}{6}}$$

Calculate 16 to the power of -\frac{3}{2} and get \frac{1}{64}.

$$\left(\frac{1}{15625}\times \frac{1}{64}\right)^{-\frac{1}{6}}$$

Multiply \frac{1}{15625} and \frac{1}{64} to get \frac{1}{1000000}.

$$\left(\frac{1}{1000000}\right)^{-\frac{1}{6}}$$

Calculate \frac{1}{1000000} to the power of -\frac{1}{6} and get 10.

$$10$$

Factor

$$2\times 5$$