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

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Question

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

$10$

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 $\frac{1}{1000000}$.

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

Fraction $\frac{-1}{6}$ can be rewritten as $-\frac{1}{6}$ by extracting the negative sign.

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

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

$$10$$

$2\times 5$