Question

can anyone answer my question please help me​

Answer 1

Answer:

Step-by-step explanation:

70-9

Answer 2

1. Evaluate :-

$\tt (i) \: {3}^{ - 4} = { \bigg(\dfrac{1}{3}\bigg)}^{4} \\ \\ \tt \implies { \bigg(\dfrac{1}{3}\bigg)}^{4} = { \bigg(\dfrac{1}{3}\bigg)} \times { \bigg(\dfrac{1}{3}\bigg)} \times { \bigg(\dfrac{1}{3}\bigg)} \times { \bigg(\dfrac{1}{3}\bigg)} \\ \\ \tt \implies {3}^{ - 4} = { \bigg(\dfrac{1}{81}\bigg)} \\ \\ \tt ( ii) \: {( - 4)}^{3} = - 4 \times - 4 \times - 4 \\ \\ \tt \implies - 4 \times - 4 \times - 4 = - 64 \\ \\ \\ \tt (iii) \: \: ( {\dfrac{3}{4})}^{ - 2} = ( {\dfrac{4}{3})}^{ 2} \\ \\ \tt \implies ( {\dfrac{4}{3})}^{ 2} = {\dfrac{4}{3}} \times {\dfrac{4}{3}}\\ \\ \tt \implies {\dfrac{4}{3}} \times {\dfrac{4}{3}} = \dfrac{16}{9} \\ \\ \\ \tt (iv) \: \: {(\dfrac{ - 2}{3} )}^{ - 5} = {(\dfrac{ - 3}{2} )}^{ 5}\\ \\ \tt \implies{(\dfrac{ - 3}{2} )}^{ 5} = \dfrac{ - 3}{2} \times \dfrac{ - 3}{2} \times \dfrac{ - 3}{2} \times \dfrac{ - 3}{2} \times \dfrac{ - 3}{2} \\ \\ \tt \implies \: \frac{ - 243}{32} \\ \\ \tt (v) \: \: { (\dfrac{5}{7}) }^{0} = 1$

2. Evaluate :-

$\longrightarrow { \bigg[ {\bigg( \dfrac{ - 2}{3}\bigg )}^{3} \bigg]}^{ - 2} = {\bigg( \dfrac{ - 2}{3}\bigg )}^{ - 6} \\ \\ \longrightarrow {\bigg( \dfrac{ - 2}{3}\bigg )}^{ - 6} = {\bigg( \dfrac{ - 3}{2}\bigg )}^{ 6}\\ \\ \longrightarrow {\bigg( \dfrac{ - 3}{2}\bigg )}^{ 6} = \dfrac{729}{64}$

3. Simplify :-

$\sf \longrightarrow ({3}^{ - 1} + {6}^{ - 1} ) \div {(\dfrac{3}{4} )}^{ - 1} \\ \\ \sf \longrightarrow ( \dfrac{1}{3} + \dfrac{1}{6} ) \div {(\dfrac{4}{3} )}\\ \\ \sf \longrightarrow ( \dfrac{2 + 1}{6} ) \div {(\dfrac{4}{3} )} = ( \dfrac{3}{6} ) \div {(\dfrac{4}{3} )} \\ \\ \longrightarrow ( \dfrac{3}{6} ) \times {(\dfrac{3}{4} )} = \dfrac{3}{8}$

4. By what number should..... ?

$\tt \: let \: the \: number \: be \: \bold{x}. \\ \\ \tt \rightarrow \: according \: to \: the \: question : \\ \\ \tt \implies {\bigg( \dfrac{ - 2}{3} \bigg)}^{ - 3} \div x = {\bigg( \dfrac{4}{9} \bigg)}^{ - 2} \\ \\ \tt \implies {\bigg( \dfrac{ - 2}{3} \bigg)}^{ - 3} \times \dfrac{1}{x} = {\bigg( {(\dfrac{2}{3})}^{2} \bigg)}^{ - 2} \\ \\ \tt \implies {\bigg( \dfrac{ - 2}{3} \bigg)}^{ - 3} = {\bigg( {\dfrac{2}{3}} \bigg)}^{ - 4} x\\ \\ \tt \implies \frac{{\bigg( \dfrac{ - 2}{3} \bigg)}^{ - 3}}{{\bigg( {\dfrac{2}{3}} \bigg)}^{ - 4}} = x \\ \\ \tt \implies \dfrac{ - 2}{3} = x \\ \\ \tt \therefore \: answer \: is \: = \dfrac{ - 2}{3}$

5. By what number should ......... ?

$\tt let \: the \: number \: be \: \bold{x} . \\ \\ \tt according \: to \: the \: question : \\ \\ \tt \rightarrow{( - 3)}^{ - 1} x = {6}^{ - 1} \\ \\ \rightarrow \tt \dfrac{ - 1}{3} \times x = \dfrac{ 1}{6}\\ \\ \rightarrow \tt x = \dfrac{ 1}{6} \times ( - 3) = \dfrac{ - 1}{2}$

6. Express each .......... form.

$\tt( i)345 = 3.45 \times {10}^{2} \\ \\ \tt(ii)180000 = 1.8 \times {10}^{5} \\ \\ \tt(iii)0.000003 = 3 \times {10}^{ - 6} \\ \\ \tt(iv)0.000027 = 2.7 \times {10}^{ - 5}$