1. $7^6 \div 7^4 = 7^{6-4} = 7^2$
2. $4^1 \div 4^0 = 4^{1-0} = 4^1 = 4$
3. $2^6 \cdot 2^{-9} = 2^{6+(-9)} = 2^{-3} = \frac{1}{2^3}$
4. $((-4)^9)^9 = (-4)^{9 \cdot 9} = (-4)^{81}$
5. $\frac{3^2}{3^3} = 3^{2-3} = 3^{-1} = \frac{1}{3}$
6. $(-4)^7 \cdot (-8)^7 = ((-4) \cdot (-8))^7 = 32^7$
7. $\frac{(-2)^{-8}}{(-2)^{-1}} = (-2)^{-8-(-1)} = (-2)^{-7} = \frac{1}{(-2)^7}$
8. $(-8)^2 \cdot (-8)^{-5} = (-8)^{2+(-5)} = (-8)^{-3} = \frac{1}{(-8)^3}$
9. $(-5)^{-4} \cdot 3^{-4} = ((-5) \cdot 3)^{-4} = (-15)^{-4} = \frac{1}{(-15)^4}$
10. $(6^{-9})^1 = 6^{-9 \cdot 1} = 6^{-9} = \frac{1}{6^9}$
Parent Tip: Review the logic above to help your child master the concept of law of exponents worksheet.
