Question

simplify exponents and powers 12⁴X9³X4 /(over/upon). 6³X8²X 27 pls explain the answer​

Answer 1

Answer:

$\frac{ {12}^{4} \times {9}^{3} \times 4 }{ {6}^{3} \times {8}^{2} \times 27} \\ = \frac{ {(3 \times 2 \times 2)}^{4} \times { ({3}^{2}) }^{3} \times {2}^{2} }{ {(3 \times 2)}^{3} \times {( {2}^{3}) }^{2} \times {3}^{3} } \\ = \frac{( {3}^{4} \times {2}^{4} \times {2}^{4} ) \times {3}^{2 \times 3} \times {2}^{2} }{( {3}^{3} \times {2}^{3}) \times {2}^{3 \times 2} \times {3}^{3} } \\ = \frac{ {3}^{4} \times {2}^{4} \times {2}^{4} \times {3}^{6} \times {2}^{2} }{ {3}^{3} \times {2}^{3} \times {2}^{6} \times {3}^{3}} \\ = \frac{ {(3)}^{4 + 6} \times {(2)}^{4 + 4 + 2} }{ {(3)}^{3 + 3} \times {(2)}^{3 + 6} } \\ = \frac{ {3}^{10} \times {2}^{10} }{ {3}^{6} \times {2}^{9} } \\ = {(3)}^{10 - 6} \times {(2)}^{10 - 9} \\ = {3}^{4} \times {2}^{1} \\ = 81 \times 2 \\ \boxed{= \underline{ \underline{ 162}}}$

Remember these points while solving like this problems :

$(a \times b)^3 = a^3 \times b^3 \\ \frac{a^6}{a^4} = a^{6-4} = a^2 \\ a^6 \times a^3 = a^{6+3} = a^9 \\ {({a}^{3})}^{2} = a^{3 \times 2} = a^6$

Hope, you understood the above solution