Question

simplify: $(-4ab^{-5})^{-2}$.$\frac{b^{10}}{16a^{2}}$$\frac{b^{25}}{16a^{2}}$$\frac{1}{16a^{2}b^{10}}$$\frac{a^{2}}{16b^{10}}$

Explanation:

Step1: Apply power of a product rule

$$(-4ab^{-5})^{-2} = (-4)^{-2} \cdot a^{-2} \cdot (b^{-5})^{-2}$$

Step2: Simplify each term

$$(-4)^{-2} = \frac{1}{(-4)^2} = \frac{1}{16}, \quad a^{-2} = \frac{1}{a^2}, \quad (b^{-5})^{-2} = b^{(-5)\times(-2)} = b^{10}$$

Step3: Multiply simplified terms

$$\frac{1}{16} \cdot \frac{1}{a^2} \cdot b^{10} = \frac{b^{10}}{16a^2}$$

Answer:

$\boldsymbol{\frac{b^{10}}{16a^2}}$ (corresponding to the first option)