Math, asked by shibusharma200822, 1 month ago

plz answer this full sheet in 30 mins plz fast ​

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Answers

Answered by Anonymous
6

Step-by-step explanation:

(a) \:  \: 0.002 \times 0.006

 \frac{2}{1000}  \times  \frac{6}{1000}

 \frac{2}{ {10}^{3} }  \times  \frac{6}{ {10}^{3} }

2 \times  {10}^{ - 3}  \times 6 \times  {10}^{ - 3}

2 \times 6 \times  {10}^{ - 3}  \times  {10}^{ - 3}

12 \times  {10}^{ - 6}

(b) \:  \:  \: 2.67004 \times  {10}^{ - 3}

 \frac{2.67004}{ {10}^{3} }

 \frac{2.67004}{1000}

0.00267004

2.(a) \:  \:  \: ( {2})^{ - 4}  \times  (\frac{5}{4} )^{4}

\frac{1 }{ 2⁴ } ×\frac{{5}^{4} }{ {4}^{4} }

 \frac{1}{ 16} \times  \frac{ {5}^{4} }{ 4⁴}

 \frac{1}{ 4²} \times  \frac{ {5}^{4} }{ 4⁴}

 \frac{ {5}^{4} }{ {4}^{4+2}}

 \frac{ {5}^{4} }{{4}^{6}} [/tex</h3><p></p><p>Answer : False</p><p></p><h3>[tex] (b) \:  \: 5.6 \times  {10}^{ - 6}  - 3.48 \times  {10}^{ - 9}

 5.6 \times  {10}^{ - 6}  - 3.48 \times  {10}^{ - 6}  \times  {10}^{ - 3}

 5.6 \times  {10}^{ - 6}  -  \frac{3.48 \times  {10}^{ - 6} }{{10}^{ - 3} }

 5.6 \times  {10}^{ - 6}  -0.00348 \times   {10}^{ - 6}

 {10}^{ - 6}  \times (5.6 - 0.00348)

 {10}^{ - 6}  \times 5.59652

or \:  \:  \:  \:  \: 5.59652 \times  {10}^{ - 6}

3. \:  \:  \because \:  {5}^{x}  =  {125}^{ - 1}

 {5}^{x}  = ( {5^{3} })^{ - 1}

 {5}^{x}  =  {5}^{3( - 1)}

 {5}^{x}  =  {5}^{ - 3}

 \therefore \:  \: x =  - 3

(a) \:  \:  {2}^{x}

 {2}^{ - 3}

  \frac{1}{ {2}^{3} }

 \frac{1}{8}

(b) \:  \:  \:  {3}^{x}  \times  {4}^{x}

 {3}^{ - 3}  \times  {4}^{ - 3}

 \frac{1}{ {3}^{3} }  \times  \frac{1}{ {4}^{3} }

 \frac{1}{27}  \times  \frac{1}{64}

 \frac{1}{576}

4. \:  \:  \frac{125}{128}  \times ( \frac{2}{5} )^{6}  \times ( \frac{ - 5}{8} )^{ - 3}

  \frac{125}{128}  \times  \frac{ {2}^{6} }{5^{6}}  \times ( \frac{ (-1 ) \times   5}{8} )^{ - 3}

   \scriptsize\frac{125}{128}  \times  \frac{ {2} \times 2 \times 2 \times 2 \times 2 \times 2}{5 \times 5 \times 5 \times 5 \times 5 \times 5} \times\frac{ (-1 ) ^{ - 3}  \times 5 ^{ - 3} }{8^{ - 3} }

 \frac{125}{128}  \times  \frac{64}{125 \times 125}  \times  \frac{ - 1 \times ( - 125)}{  64 \times( -  8)}

 \frac{ \cancel{125}}{128}  \times  \frac{64}{ \cancel{125} \times 125}  \times  \frac{ - 1 \times ( - 125)}{  64 \times( -  8)}

 \frac{ 1}{128}  \times \frac{ \cancel{64}}{ \cancel{125}}   \times  \frac{ \cancel{125}}{ \cancel{64 }\times ( - 8)}

 \frac{1}{128}  \times  \frac{1}{ - 8}

 \frac{1}{−1024}

(b) \:  \: Let \: \:   that \: \:   number \:   \: be  \: \:  X.

According to the question,

( \frac{1}{9} )^{ -2}  \times x = ( \frac{3}{8} )^{ - 4}

({9})^{2}  \times x = ( \frac{8}{3}) ^{4}

81 \times x =  \frac{4096}{81}

x =  \frac{4096}{81}  \times  \frac{1}{81}

x =  \frac{4096}{6561}

x =  \frac{ {8}^{4} }{ {9}^{4} }

Answered by Anonymous
1

(a)0.002×0.006

\frac{2}{1000} \times \frac{6}{1000}

1000

2

×

1000

6

\frac{2}{ {10}^{3} } \times \frac{6}{ {10}^{3} }

10

3

2

×

10

3

6

2 \times {10}^{ - 3} \times 6 \times {10}^{ - 3}2×10

−3

×6×10

−3

2 \times 6 \times {10}^{ - 3} \times {10}^{ - 3}2×6×10

−3

×10

−3

12 \times {10}^{ - 6}12×10

−6

(b) \: \: \: 2.67004 \times {10}^{ - 3}(b)2.67004×10

−3

\frac{2.67004}{ {10}^{3} }

10

3

2.67004

\frac{2.67004}{1000}

1000

2.67004

0.002670040.00267004

2.(a) \: \: \: ( {2})^{ - 4} \times (\frac{5}{4} )^{4}2.(a)(2)

−4

×(

4

5

)

4

\frac{1 }{ 2⁴ } ×\frac{{5}^{4} }{ {4}^{4} }

2⁴

1

×

4

4

5

4

\frac{1}{ 16} \times \frac{ {5}^{4} }{ 4⁴}

16

1

×

4⁴

5

4

\frac{1}{ 4²} \times \frac{ {5}^{4} }{ 4⁴}

1

×

4⁴

5

4

\frac{ {5}^{4} }{ {4}^{4+2}}

4

4+2

5

4

\frac{ {5}^{4} }{{4}^{6}} [/tex < /h3 > < p > < /p > < p > Answer : False < /p > < p > < /p > < h3 > [tex] (b) \: \: 5.6 \times {10}^{ - 6} - 3.48 \times {10}^{ - 9}

4

6

5

4

[/tex</h3><p></p><p>Answer:False</p><p></p><h3>[tex](b)5.6×10

−6

−3.48×10

−9

5.6 \times {10}^{ - 6} - 3.48 \times {10}^{ - 6} \times {10}^{ - 3}5.6×10

−6

−3.48×10

−6

×10

−3

5.6 \times {10}^{ - 6} - \frac{3.48 \times {10}^{ - 6} }{{10}^{ - 3} }5.6×10

−6

10

−3

3.48×10

−6

5.6 \times {10}^{ - 6} -0.00348 \times {10}^{ - 6}5.6×10

−6

−0.00348×10

−6

{10}^{ - 6} \times (5.6 - 0.00348)10

−6

×(5.6−0.00348)

{10}^{ - 6} \times 5.5965210

−6

×5.59652

or \: \: \: \: \: 5.59652 \times {10}^{ - 6}or5.59652×10

−6

3. \: \: \because \: {5}^{x} = {125}^{ - 1}3.∵5

x

=125

−1

{5}^{x} = ( {5^{3} })^{ - 1}5

x

=(5

3

)

−1

{5}^{x} = {5}^{3( - 1)}5

x

=5

3(−1)

{5}^{x} = {5}^{ - 3}5

x

=5

−3

\therefore \: \: x = - 3∴x=−3

(a) \: \: {2}^{x}(a)2

x

{2}^{ - 3}2

−3

\frac{1}{ {2}^{3} }

2

3

1

\frac{1}{8}

8

1

(b) \: \: \: {3}^{x} \times {4}^{x}(b)3

x

×4

x

{3}^{ - 3} \times {4}^{ - 3}3

−3

×4

−3

\frac{1}{ {3}^{3} } \times \frac{1}{ {4}^{3} }

3

3

1

×

4

3

1

\frac{1}{27} \times \frac{1}{64}

27

1

×

64

1

\frac{1}{576}

576

1

4. \: \: \frac{125}{128} \times ( \frac{2}{5} )^{6} \times ( \frac{ - 5}{8} )^{ - 3}4.

128

125

×(

5

2

)

6

×(

8

−5

)

−3

\frac{125}{128} \times \frac{ {2}^{6} }{5^{6}} \times ( \frac{ (-1 ) \times 5}{8} )^{ - 3}

128

125

×

5

6

2

6

×(

8

(−1)×5

)

−3

\scriptsize\frac{125}{128} \times \frac{ {2} \times 2 \times 2 \times 2 \times 2 \times 2}{5 \times 5 \times 5 \times 5 \times 5 \times 5} \times\frac{ (-1 ) ^{ - 3} \times 5 ^{ - 3} }{8^{ - 3} }

128

125

×

5×5×5×5×5×5

2×2×2×2×2×2

×

8

−3

(−1)

−3

×5

−3

\frac{125}{128} \times \frac{64}{125 \times 125} \times \frac{ - 1 \times ( - 125)}{ 64 \times( - 8)}

128

125

×

125×125

64

×

64×(−8)

−1×(−125)

\frac{ \cancel{125}}{128} \times \frac{64}{ \cancel{125} \times 125} \times \frac{ - 1 \times ( - 125)}{ 64 \times( - 8)}

128

125

×

125

×125

64

×

64×(−8)

−1×(−125)

\frac{ 1}{128} \times \frac{ \cancel{64}}{ \cancel{125}} \times \frac{ \cancel{125}}{ \cancel{64 }\times ( - 8)}

128

1

×

125

64

×

64

×(−8)

125

\frac{1}{128} \times \frac{1}{ - 8}

128

1

×

−8

1

\frac{1}{−1024}

−1024

1

(b) \: \: Let \: \: that \: \: number \: \: be \: \: X.(b)LetthatnumberbeX.

According to the question,

( \frac{1}{9} )^{ -2} \times x = ( \frac{3}{8} )^{ - 4}(

9

1

)

−2

×x=(

8

3

)

−4

({9})^{2} \times x = ( \frac{8}{3}) ^{4}(9)

2

×x=(

3

8

)

4

81 \times x = \frac{4096}{81}81×x=

81

4096

x = \frac{4096}{81} \times \frac{1}{81}x=

81

4096

×

81

1

x = \frac{4096}{6561}x=

6561

4096

x = \frac{ {8}^{4} }{ {9}^{4} }x=

9

4

8

4

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