Since the user options for ExplainAnswer, TeachTopic, and GeneratePractice are all set to false, I will proceed directly to providing the final answers for each section of the worksheet.
Final Answer:
Section A
1) 1
2) -8
3) 1
4) 343
5) -161
6) 9/16
Section B
1) $5^6$
2) $9^{13}$
3) $2^6$
4) $8^5$
5) $7^2$
6) $12^4$
7) $4^{20}$
8) 1
9) $2^5$
10) $6^{-8}$ or $\frac{1}{6^8}$
11) $15^{-7}$ or $\frac{1}{15^7}$
12) $7^{-3}$ or $\frac{1}{7^3}$
Section C
1) $2^6$
2) $8^{-3}$ or $\frac{1}{8^3}$
3) $10^{-19}$ or $\frac{1}{10^{19}}$
4) $3^{-5}$ or $\frac{1}{3^5}$
5) $3^6$
6) $6^8$
7) $7^{-11}$ or $\frac{1}{7^{11}}$
8) $14^{31}$
9) $4^7$
10) $6^2$
11) $20^{10}$
12) $\frac{2e^7}{5}$ (Note: Assuming 'e' is a variable here. If 'e' represents Euler's number, the expression simplifies numerically but usually in algebraic contexts like this, it's treated as a variable).
Extension
*Investigate the following:*
$(2^1)^2 = 2^2$
$(2^2)^2 = 2^4$
$(2^3)^2 = 2^6$
$(2^4)^2 = 2^8$
$(2^5)^2 = 2^{10}$
$(5^1)^3 = 5^3$
$(5^2)^3 = 5^6$
$(5^3)^3 = 5^9$
$(5^4)^3 = 5^{12}$
$(5^5)^3 = 5^{15}$
*Use your results to simplify:*
$(4^2)^4 = 4^8$
$(6^3)^8 = 6^{24}$
$(9^{-5})^6 = 9^{-30}$
$(11^{-2})^{-7} = 11^{14}$
Parent Tip: Review the logic above to help your child master the concept of multiplying powers with the same base worksheet.
