Question

2. Simplify:
i) 4 x 12^4 x 9^3
27 x 8^2 x 6^3
Pls solve it​

Answer 1

Answer:

$4 \times {12}^{4} \times {9}^{3} \\ = {2}^{2} \times {(4 \times 3)}^{4} \times { ({3}^{2}) }^{3} \\ = {2}^{2} \times {( {2}^{2} \times 3)}^{4} \times { {(3}^{2} )}^{3} \\ = {2}^{2} \times {( {2}^{2}) }^{4} \times {3}^{4} \times {(3)}^{2 \times 3} \\ = {2}^{2} \times {(2)}^{2 \times 4} \times {3}^{4} \times {3}^{6} \\ = {2}^{2} \times {2}^{8} \times {3}^{4} \times {3}^{6} \\ = {(2)}^{2 + 8} \times {(3)}^{4 + 6} \\ = \underline{ \underline{ {2}^{10} \times {3}^{10} }} \\ \\ 27 \times {8}^{2} \times {6}^{3} \\ = {3}^{3} \times { ({2}^{3}) }^{2} \times {(2 \times 3)}^{3} \\ = {3}^{3} \times {(2)}^{3 \times 2} \times {2}^{3} \times {3}^{3} \\ = {3}^{3} \times {2}^{6} \times {2}^{3} \times {3}^{3} \\ = {(2)}^{6 + 3} \times {(3)}^{3 + 3} \\ = \underline{ \underline{{2}^{9} \times {3}^{6} }} \\ \\ \large{ \underline{ Note} : } \\ * \: \: \: {( {a}^{m} )}^{n} = {(a)}^{m \times n} \\ * \: \: \: {(a \times b)}^{m} = {a}^{m} \times {b}^{m} \\ * \: \: \: {a}^{m} \times {a}^{n} = {(a)}^{m + n}$