Question
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. \( 22^{10} \div 22^{8} \) \( \qquad \) \( = \) \( \qquad \)
Ask by Mathis Wilson. in the Philippines
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
11. \( 5^{7} \div 5^{4} = 125 \)
12. \( \left(2^{3} \times 2^{2}\right) \div \left(2^{2} \times 2^{2}\right) = 2 \)
13. \( \left(7^{8} \div 7^{4}\right) \times \left(7^{10} \div 7^{8}\right) = 117649 \)
14. \( 10^{6} \div 10^{4} = 100 \)
15. \( \frac{a^{15}}{a^{2}} = a^{13} \)
16. \( \frac{\left(10^{2}\right) \left(10^{7}\right)}{10^{5}} = 10000 \)
17. \( \frac{4^{7}}{4^{7}} = 1 \)
18. \( \frac{20^{9}}{20} = 25,\!600,\!000,\!000 \)
19. \( \left(11 \times 11^{5}\right) \div 11^{2} = 14,\!641 \)
20. \( 22^{10} \div 22^{8} = 484 \)
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To add some fun behind the equations of exponents, let’s delve into how these mathematical manipulations aren't just abstract numbers but have real-life applications! Exponential growth is seen in everything from population studies to compound interest in finance. Whenever you double down on your investments, envision those numbers growing exponentially in your bank account! Now, when working with exponents, one common pitfall is misapplying the rules, especially with division and multiplication. Remember, when dividing powers of the same base, you subtract the exponents (like \( a^m \div a^n = a^{m-n} \)). It's easy to mix this up, so take a moment to double-check your steps and keep those rules in mind to avoid frustrating errors!
