Question

Simplify:
1. [(15/12)^3]^4

2. (3^4)^-2

3. [(1/7)^-3]^4

4. [(2/5)^-2]-3

5. (65)^4

6. [(6/7)^5]^2

7. [(2/3)^-4]^5

8. [(5/8)^3]^-2

9. [(3/4)^6]^1

10. [(2/5)^-3]^2

Answer 1

Simplify:

$\sf{1. \; \bigg [\bigg(\dfrac{15}{12}\bigg)^3\bigg]^4}$

$:\implies \; \sf{\bigg(\dfrac{15}{12}\bigg)^{3 \times 4}}\\\\:\implies \; \sf{\bigg(\dfrac{15}{12}\bigg)^{12}}$

____

$\sf{2. \; (3^4)^{-2}}$

$:\implies \; \sf{(3)^{4 \times 2}}\\\\:\implies \; \sf{(3)^{-8}}$

____

$\sf{ 3. \; \bigg[\bigg(\dfrac{1}{7}\bigg)^{-3}\bigg]^4}$

$:\implies \; \sf{\bigg(\dfrac{1}{7}\bigg)^{(-3) \times 4}}$

$:\implies \; \sf{\bigg( \dfrac{1}{7}\bigg)^{-12}}$

____

$\sf{4. \; \bigg[ \bigg( \dfrac{2}{5}\bigg)^{-2}\bigg]^{-3}}$

$:\implies \; \sf{\bigg(\dfrac{2}{5}\bigg)^{(-2) \times (-3)}}$

$:\implies \; \sf{\bigg( \dfrac{2}{5}\bigg)^{6}}$

____

$\sf{5. \; (65)^4}$

$:\implies \; \sf{(6)^{5 \times 4}}\\\\:\implies \; \sf{(6)^{20}}$

____

$\sf{6. \; \bigg[\bigg(\dfrac{6}{7}\bigg)^5\bigg]^2}$

$:\implies \; \sf{\bigg(\dfrac{6}{7}\bigg)^{5 \times 2}}\\\\:\implies \; \sf{\bigg(\dfrac{6}{7}\bigg)^{10}}$

____

$\sf{7. \; \bigg[\bigg(\dfrac{2}{3}\bigg)^{-4}\bigg]^5}$

$:\implies \; \sf{\bigg(\dfrac{2}{3}\bigg)^{(-4) \times 5}}\\\\:\implies \; \sf{\bigg(\dfrac{2}{3}\bigg)^{-20}}$

____

$\sf{8. \; \bigg[\bigg(\dfrac{5}{8}\bigg)^{3} } }$

$:\implies \; \sf{\bigg(\dfrac{5}{8}\bigg)^{3 \times (-2)}}\\\\:\implies \; \sf{\bigg(\dfrac{5}{8}\bigg)^{-6}}$

____

$\sf{9. \; \bigg[\bigg(\dfrac{3}{4}\bigg)^6\bigg]^1}$

$:\implies \; \sf{\bigg(\dfrac{3}{4} \bigg)^{6 \times 1}}\\\\:\implies \; \sf{\bigg(\dfrac{3}{4}\bigg)^{6 }}$

____

$\sf{10.\; \bigg[\bigg(\dfrac{2}{5}\bigg)^{-3}\bigg]^2}$

$:\implies \; \sf{\bigg(\dfrac{2}{5} \bigg)^{(-3) \times 2}}\\\\:\implies \; \sf{\bigg(\dfrac{2}{5}\bigg)^{(-6)}}$

━━━━━━━━━━━━━━━━━━━

Apologies for the mistakes <3