1. **State the problem:** We need to write 4 expressions equal to $$\frac{8a^{16}}{ab^{10}}$$ each using a different power law from the given four: - $$x^m / x^n = x^{m-n}$$ - $$x^m \cdot x^n = x^{m+n}$$ - $$x^{-m} = \frac{1}{x^m}$$ - $$x^0 = 1$$ 2. **Simplify the original expression:** $$\frac{8a^{16}}{ab^{10}} = 8 \cdot \frac{a^{16}}{a} \cdot \frac{1}{b^{10}} = 8a^{16-1}b^{-10} = 8a^{15}b^{-10}$$ 3. **Expression using the division power law $$x^m / x^n = x^{m-n}$$:** $$8a^{16}b^{-10} \cdot a^{-1} = 8a^{16-1}b^{-10} = 8a^{15}b^{-10}$$ 4. **Expression using the multiplication power law $$x^m \cdot x^n = x^{m+n}$$:** Rewrite $$8a^{15}b^{-10}$$ as $$8a^{10} \cdot a^{5} \cdot b^{-10} = 8a^{10}a^{5}b^{-10}$$ 5. **Expression using the negative exponent law $$x^{-m} = \frac{1}{x^m}$$:** $$8a^{15} \cdot b^{-10} = \frac{8a^{15}}{b^{10}}$$ 6. **Expression using the zero exponent law $$x^0 = 1$$:** Write $$a^{15} = a^{15} \cdot a^0$$ and $$b^{-10} = b^{-10} \cdot b^0$$ so $$8a^{15}b^{-10} = 8a^{15}a^0b^{-10}b^0$$ **Final four expressions:** 1. $$8a^{16}b^{-10}a^{-1}$$ 2. $$8a^{10}a^{5}b^{-10}$$ 3. $$\frac{8a^{15}}{b^{10}}$$ 4. $$8a^{15}a^0b^{-10}b^0$$