Question

Question is to simplify This ​

Answer 1

$\dfrac{ {( - 2}^{3}) \times ( { - 2}^{7}) }{3 \times {4}^{6} }$

we know that,

${a}^{m} \times {a}^{n} = {a}^{m + n}$

$\dfrac{ {( - 2}^{3 + 7}) }{3 \times ({2}^{2})^{6} }$

$( {a}^{n})^{m} = {a}^{mn}$

$\dfrac{( { - 2}^{10})}{3 \times ( {2}^{12}) }$

$\dfrac{1}{3} \times \dfrac{{ - 2}^{10} }{ {2}^{12} }$

as the power is even,

$\dfrac{1}{3}$  × $\dfrac{2^{10} }{2^{12} }$

$a^{m}$ ÷ $a^{n} = a^{m-n}$

$\dfrac{1}{3}$ × $2^{10-12}$

$\dfrac{1}{3}$ × 2⁻²

$a^{-m} = \dfrac{1}{a^{m} }$

$\dfrac{1}{3}$ × $\dfrac{1}{2^{2} }$

$\dfrac{1}{3}$ × $\dfrac{1}{4}$

Answer => $\dfrac{1}{12}$

Important points to remember :

${a}^{m} \times {a}^{n} = {a}^{m + n}$

${a}^{m} \times {b}^{m} = {ab}^{m}$

${a}^{m} \div {a}^{n} = {a}^{m - n}$

${a}^{m} \div {b}^{m} = (\frac{ a}{b}) ^{m}$

${a}^{ - m} = \frac{1}{ {a}^{m} }$

Answer 2

Answer:

Hope you get the answer of your question☺️ and also the answer are correct❤️