plz answer this full sheet in 30 mins plz fast
Answers
Step-by-step explanation:
According to the question,
(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}
4²
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