Question

first to answer proper gets brainliest​

Answer 1

Answer:

1 i)1/9

ii)1/16

iii) 32

2 i) -64

ii) 1/64

iii) 625

iv) 1/9

v) 1/-2744

3 i) 5

ii) 1/2

iii) 29

Answer 2

Step-by-step explanation:

Evaluate:-

${3}^{ - 2}$

$⟹ ( \frac{3}{1} ) ^{ - 2}$

$⟹( \frac{1}{3} {)}^{2}$

$⟹ \frac{1 \times 1 }{3 \times 3}$

$⟹ \tt \red{ \frac{1}{9} } \: \: ans.$

$( - 4)^{ - 2}$

$⟹( \frac{ - 4}{1} )^{ - 2}$

$⟹( \frac{1}{4} )^{2}$

$⟹ \frac{1 \times 1}{4 \times 4}$

$⟹ \tt \red{ \frac{1}{16} } \: \: ans.$

$( \frac{1}{2} ) ^{ - 5}$

$⟹( \frac{2}{1} )^{5}$

$⟹ \frac{2 \times 2 \times 2 \times 2 \times 2}{1 \times 1 \times 1 \times 1 \times 1}$

$⟹ \tt \red{\frac{32}{1} } \: \: ans.$

Simplify and express the result in power notation with positive exponent:-

$( - 4 {)}^{5} + ( - 4 {)}^{8}$

$⟹ \frac{( - 4 {)}^{5} }{( - 4 {)}^{8} }$

$⟹( - 4 {)}^{5 - 8}$

$⟹( - 4 {)}^{ - 3}$

$⟹ \frac{1}{( - 4 {)}^{3} }$

$( \frac{1}{ - {2}^{3} } {)}^{2}$

$⟹ \frac{1}{ {2}^{3 \times 2} }$

$⟹ \tt \red{\frac{1}{ {2}^{6} }} \: \: ans.$

$( - 3 {)}^{4} \times ( \frac{5}{3} {)}^{4}$

$⟹( - 1 {)}^{4} \times (3 {)}^{4} \times ( \frac{5}{3} ) ^{4}$

$⟹( - 1 {)}^{4} \times {5}^{4}$

$⟹ \tt \red{ {5}^{4} } \: \: ans.$

$( {3}^{ - 7} \div {3}^{ - 10} ) \times {3}^{ - 5}$

$⟹( \frac{ {3}^{ - 7} }{ {3}^{ - 10} } ) \times (3 {)}^{ - 5}$

$⟹ {3}^{ - 7 + 10} \times {3}^{ - 5}$

$⟹ {3}^{3} \times {3}^{ - 5}$

$⟹ {3}^{3 - 5}$

$⟹ {3}^{ - 2}$

$⟹ \tt \red{\frac{1}{ {3}^{2} }} \: \: ans.$

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

$⟹ \frac{1}{ {2}^{3} } \times \frac{1}{( - 3)^{3} }$

=> $\underline{{\left({\frac{1}{{2}\mathrm{\times}{\mathrm{(}}\mathrm{{-}}{7}{\mathrm{)}}}}\right)}^{2}}$

=> $\frac{1}{{\mathrm{(}}\mathrm{{-}}{\mathrm{14}}{\mathrm{)}}^{3}}$ Ans.

Find the value of:-

$\left({{3}^{0}\mathrm{{+}}{4}^{\mathrm{{-}}{1}}}\right)$ × 2²

=> $\left({\frac{{1}\mathrm{{+}}{1}}{4}}\right)$ × 4

=> $\frac{5}{4}$ × 4

=> 5 Ans.

$\left({{2}^{\mathrm{{-}}{1}}\mathrm{\times}{4}^{\mathrm{{-}}{1}}}\right)$ ÷ 2-²

=> $\left({\frac{1}{2}\mathrm{\times}\frac{1}{4}}\right)$ ÷ $\frac{1}{{2}^{2}}$

=> $\frac{1}{8}$ ÷ $\frac{1}{4}$

=> $\frac{1}{8}$ × $\frac{4}{1}$

=> $\frac{1}{2}$ Ans.