11. \( 5^{7} \div 5^{4}= \) \( \qquad \) 12. \( \left(2^{3} \times 2^{2}\right) \div\left(2^{2} \times 2^{2}\right)= \) \( \qquad \) \( = \) \( \qquad \) 13. \( \left(7^{8} \div 7^{4}\right) \times\left(7^{10} \div 7^{8}\right)= \) \( \qquad \) \( = \) \( \qquad \) 14. \( 10^{6} \div 10^{4}= \) \( \qquad \) \( = \) \( \qquad \) 15. \( \frac{a^{15}}{a^{2}} \), where \( a \neq 0= \) \( \qquad \) \( \qquad \) 16. \( \frac{\left(10^{2}\right)\left(10^{7}\right)}{10^{5}}= \) \( \qquad \) \( = \) \( \qquad \) 17. \( \frac{4^{7}}{4^{7}} \) \( = \) \( \qquad \) \( = \) \( \qquad \) 18. \( \frac{20^{9}}{20}= \) \( \qquad \) \( = \) \( \qquad \) 19. \( \left(11 \times 11^{5}\right) \div 11^{2} \) \( \qquad \) \( = \) \( \qquad \) 20. \( 22^{10} \div 22^{8} \) \( \qquad \) \( = \) \( \qquad \)

Sure! Let's solve each of the exponent problems step by step. --- **11.** \( 5^{7} \div 5^{4} \) **Solution:** \[ 5^{7} \div 5^{4} = 5^{7-4} = 5^{3} = 125 \] **Answer:** \[ 125 \] --- **12.** \( \left(2^{3} \times 2^{2}\right) \div \left(2^{2} \times 2^{2}\right) \) **Solution:** \[ 2^{3} \times 2^{2} = 2^{3+2} = 2^{5} \] \[ 2^{2} \times 2^{2} = 2^{2+2} = 2^{4} \] \[ \frac{2^{5}}{2^{4}} = 2^{5-4} = 2^{1} = 2 \] **Answer:** \[ 2^{1} = 2 \] --- **13.** \( \left(7^{8} \div 7^{4}\right) \times \left(7^{10} \div 7^{8}\right) \) **Solution:** \[ 7^{8} \div 7^{4} = 7^{8-4} = 7^{4} \] \[ 7^{10} \div 7^{8} = 7^{10-8} = 7^{2} \] \[ 7^{4} \times 7^{2} = 7^{4+2} = 7^{6} = 117649 \] **Answer:** \[ 7^{6} = 117649 \] --- **14.** \( 10^{6} \div 10^{4} \) **Solution:** \[ 10^{6} \div 10^{4} = 10^{6-4} = 10^{2} = 100 \] **Answer:** \[ 10^{2} = 100 \] --- **15.** \( \frac{a^{15}}{a^{2}} \), where \( a \neq 0 \) **Solution:** \[ \frac{a^{15}}{a^{2}} = a^{15-2} = a^{13} \] **Answer:** \[ a^{13} \] --- **16.** \( \frac{\left(10^{2}\right) \left(10^{7}\right)}{10^{5}} \) **Solution:** \[ 10^{2} \times 10^{7} = 10^{2+7} = 10^{9} \] \[ \frac{10^{9}}{10^{5}} = 10^{9-5} = 10^{4} = 10000 \] **Answer:** \[ 10^{4} = 10000 \] --- **17.** \( \frac{4^{7}}{4^{7}} \) **Solution:** \[ \frac{4^{7}}{4^{7}} = 4^{7-7} = 4^{0} = 1 \] **Answer:** \[ 1 \] --- **18.** \( \frac{20^{9}}{20} \) **Solution:** \[ 20 = 20^{1} \] \[ \frac{20^{9}}{20^{1}} = 20^{9-1} = 20^{8} \] \[ 20^{8} = 25,600,000,000 \] **Answer:** \[ 20^{8} = 25,\!600,\!000,\!000 \] --- **19.** \( \left(11 \times 11^{5}\right) \div 11^{2} \) **Solution:** \[ 11 \times 11^{5} = 11^{1+5} = 11^{6} \] \[ \frac{11^{6}}{11^{2}} = 11^{6-2} = 11^{4} = 14,\!641 \] **Answer:** \[ 11^{4} = 14,\!641 \] --- **20.** \( 22^{10} \div 22^{8} \) **Solution:** \[ 22^{10} \div 22^{8} = 22^{10-8} = 22^{2} = 484 \] **Answer:** \[ 22^{2} = 484 \] --- I hope this helps! If you have any more questions or need further explanations, feel free to ask.