Question

Find the value [(-2/11)4 ×(-2/11)7]÷(-2/11)9]​

Answer 1

$\large\underline{\sf{Given- }}$

$\rm :\longmapsto\: \bigg \{{\bigg( \dfrac{ - 2}{11} \bigg) }^{4} \times {\bigg( \dfrac{ - 2}{11} \bigg) }^{7} \bigg\} \div {\bigg( \dfrac{ - 2}{11} \bigg) }^{9}$

$\large\underline{\sf{Solution-}}$

Basic Concept Used :-

Here,

• Law of exponents are used :-

$1. \: \: \: \: \boxed{ \sf{ \: {a}^{x} \times {a}^{y} = {a}^{x + y} }}$

$2. \: \: \: \boxed{ \sf{ \: {a}^{x} \div {a}^{y} = {a}^{x - y}}}$

Now,

• Consider,

$\rm :\longmapsto\: \bigg \{{\bigg( \dfrac{ - 2}{11} \bigg) }^{4} \times {\bigg( \dfrac{ - 2}{11} \bigg) }^{7} \bigg\} \div {\bigg( \dfrac{ - 2}{11} \bigg) }^{9}$

$\rm :\longmapsto\: = \: \bigg \{{\bigg( \dfrac{ - 2}{11} \bigg) }^{4 + 7} \bigg\} \div {\bigg( \dfrac{ - 2}{11} \bigg) }^{9}$

$\rm :\longmapsto\: = \: \bigg \{{\bigg( \dfrac{ - 2}{11} \bigg) }^{11} \bigg\} \div {\bigg( \dfrac{ - 2}{11} \bigg) }^{9}$

$\rm :\longmapsto\: = {\bigg( \dfrac{ - 2}{11} \bigg) }^{11 - 9}$

$\rm :\longmapsto\: = \: {\bigg( \dfrac{ - 2}{11} \bigg) }^{2}$

$\rm :\longmapsto\: = \: {\bigg( \dfrac{ - 2}{11} \bigg) } \times {\bigg( \dfrac{ - 2}{11} \bigg) }$

$\rm :\longmapsto\: = \: \dfrac{4}{121}$

More Law of exponents :-

$\boxed{ \sf{ \: {a}^{0} = 1 \: provided \: that \: a \ne0}}$

$\boxed{ \sf{ \: {( {a}^{x}) }^{y} = {a}^{xy} }}$

$\boxed{ \sf{ \: {a}^{ - x} = {\bigg( \dfrac{1}{a} \bigg) }^{x}}}$

$\boxed{ \sf{ \: {a}^{x} \times {y}^{x} = {(a \times y)}^{x} }}$

$\boxed{ \sf{ \: {a}^{x} = {a}^{y} \rm :\implies\:x = y}}$

Answer 2

Answer:

here the answer mark as brainlist