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question_answer1)
Find the value of given expression: \[{{\left( \frac{5}{9} \right)}^{(-2)}}\times {{\left( \frac{3}{5} \right)}^{\left( -2 \right)}}\times {{\left( \frac{3}{5} \right)}^{(0)}}\]
A)
10 done
clear
B)
9 done
clear
C)
20 done
clear
D)
30 done
clear
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question_answer2)
Simplify: \[{{x}^{2}}{{y}^{2}}\times {{x}^{5}}{{y}^{3}}\]
A)
\[{{x}^{7}}{{y}^{5}}\] done
clear
B)
\[{{x}^{7}}{{y}^{7}}\] done
clear
C)
\[{{x}^{5}}{{y}^{5}}\] done
clear
D)
\[{{x}^{5}}{{y}^{7}}\] done
clear
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question_answer3)
The value of the expression \[\frac{{{4}^{-5}}\times {{10}^{6}}\times 625}{{{4}^{-8}}\times {{4}^{2}}}\] is given by
A)
\[2.5\times {{10}^{9}}\] done
clear
B)
\[3.5\times {{10}^{5}}\] done
clear
C)
\[4.5\times {{10}^{5}}\] done
clear
D)
\[5.5\times {{10}^{5}}\] done
clear
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question_answer4)
Find the value of m in the expression \[\frac{{{\left( 16 \right)}^{2m+1}}{{\left( 64 \right)}^{5}}}{{{\left( 256 \right)}^{2}}\times 4}={{\left( 256 \right)}^{3m}}\]
A)
1 done
clear
B)
0 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer5)
The value of \[\frac{1}{2}\left[ \frac{-7}{4}+\frac{5}{3}+\frac{-5}{6}+\frac{1}{3}+\frac{-1}{2} \right]\]\[+\frac{1}{3}\left[ \frac{-12}{5}+\frac{-7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10} \right]\] is
A)
\[\frac{1153}{840}\] done
clear
B)
\[\frac{128}{105}\] done
clear
C)
\[\frac{128}{105}\] done
clear
D)
\[\frac{-125}{256}\] done
clear
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question_answer6)
Evaluate \[{{\left[ {{\left( \sqrt{\frac{2}{3}} \right)}^{2}}-\sqrt[3]{\frac{8}{27}} \right]}^{1000}}\]
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
-1 done
clear
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question_answer7)
Simplify \[{{\left( 5a{{n}^{-2}} \right)}^{-1}}\]
A)
\[\frac{{{n}^{2}}}{5a}\] done
clear
B)
\[\frac{n}{5a}\] done
clear
C)
\[\frac{{{n}^{3}}}{5a}\] done
clear
D)
\[\frac{{{n}^{4}}}{5a}\] done
clear
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question_answer8)
Simplify \[{{\left( \frac{{{a}^{-2}}}{{{b}^{-2}}} \right)}^{-3}}\left( \frac{{{a}^{-3}}}{{{b}^{-5}}} \right)\]
A)
\[\frac{1}{{{b}^{2}}}\] done
clear
B)
\[\frac{{{a}^{3}}}{{{b}^{11}}}\] done
clear
C)
\[\frac{a}{b}\] done
clear
D)
\[\frac{{{a}^{2}}}{{{b}^{3}}}\] done
clear
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question_answer9)
Simplify \[-{{\left( 3 \right)}^{3}}-{{\left( -3 \right)}^{2}}+{{\left( -2 \right)}^{2}}\]
A)
\[-\,31\] done
clear
B)
\[-\,21\] done
clear
C)
\[-\,32\] done
clear
D)
\[-\,33\] done
clear
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question_answer10)
Find the value of x such that \[{{\left( \frac{64}{125} \right)}^{2}}{{\left( \frac{4}{5} \right)}^{4}}{{\left( \frac{16}{25} \right)}^{2x+1}}={{\left( \frac{256}{625} \right)}^{3x}}\]
A)
\[\frac{3}{2}\] done
clear
B)
\[\frac{2}{3}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer11)
By what number \[{{\left( \frac{4}{5} \right)}^{-5}}\] must be multiplied so that the result is\[\frac{16}{9}\]?
A)
\[\frac{3}{2}\] done
clear
B)
\[{{\left( \frac{4}{3} \right)}^{7}}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer12)
The scientific notation of 165000000000000 is given by
A)
\[16.5\times {{10}^{13}}\] done
clear
B)
\[165\times {{10}^{12}}\] done
clear
C)
\[1650\times {{10}^{11}}\] done
clear
D)
\[1.65\times {{10}^{14}}\] done
clear
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question_answer13)
\[\frac{{{\mathbf{8}}^{\mathbf{-1}}}\mathbf{\times }{{\mathbf{5}}^{\mathbf{3}}}}{{{\mathbf{2}}^{\mathbf{-4}}}}\]=
A)
250 done
clear
B)
325 done
clear
C)
125 done
clear
D)
100 done
clear
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question_answer14)
Find x so that \[{{\left( \frac{5}{3} \right)}^{-5}}\times {{\left( \frac{5}{3} \right)}^{-11}}={{\left( \frac{5}{3} \right)}^{8x}}\]
A)
\[-\,4\] done
clear
B)
\[-\,2\] done
clear
C)
\[-\,6\] done
clear
D)
\[-\,8\] done
clear
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question_answer15)
If \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\]then value of \[{{\mathbf{x}}^{\mathbf{2}}}\]is
A)
\[{{\left( \frac{2}{3} \right)}^{11}}\] done
clear
B)
\[{{\left( \frac{2}{3} \right)}^{12}}\] done
clear
C)
\[{{\left( \frac{2}{3} \right)}^{7}}\] done
clear
D)
\[{{\left( \frac{2}{3} \right)}^{3}}\] done
clear
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question_answer16)
The value of \[{{\left[ {{\left( \sqrt[n]{{{x}^{2}}} \right)}^{n/2}} \right]}^{2}}\]
A)
0 done
clear
B)
\[{{x}^{2}}\] done
clear
C)
\[x\] done
clear
D)
\[1/x\] done
clear
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question_answer17)
The exponential form of \[\sqrt{\sqrt{2}\times \sqrt{5}}\] is
A)
\[{{\left( 10 \right)}^{1/2}}\] done
clear
B)
\[{{10}^{1/4}}\] done
clear
C)
10 done
clear
D)
\[{{10}^{1/6}}\] done
clear
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question_answer18)
The product of \[\sqrt[3]{2}\times \sqrt[4]{3}\] is given
A)
\[\sqrt{10}\] done
clear
B)
1 done
clear
C)
\[\sqrt[12]{432}\] done
clear
D)
\[\sqrt{201}\] done
clear
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question_answer19)
If \[{{\mathbf{3}}^{-\mathbf{x}}}=\mathbf{3000},\] then find \[\mathbf{1}{{\mathbf{0}}^{\mathbf{3}}}\times {{3}^{\left( 2x+3 \right)}}\]
A)
\[3\times {{10}^{-3}}\] done
clear
B)
\[27\times {{10}^{-3}}\] done
clear
C)
\[9\times {{10}^{-3}}\] done
clear
D)
3000 done
clear
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question_answer20)
\[{{\left( \frac{{{a}^{x}}}{{{a}^{y}}} \right)}^{z}}\times {{\left( \frac{{{a}^{y}}}{{{a}^{z}}} \right)}^{x}}\times {{\left( \frac{{{a}^{z}}}{{{a}^{x}}} \right)}^{y}}=\]__________. \[\left( a\ne 0\,\mathbf{and}\,\mathbf{a}\ne 1 \right)\])
A)
1 done
clear
B)
0 done
clear
C)
\[{{a}^{xyz}}\] done
clear
D)
\[{{a}^{xy+yz+zx}}\] done
clear
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question_answer21)
\[{{\left( \frac{a}{b} \right)}^{x+y+z}}\div \left[ {{\left( \sqrt{\frac{a}{b}} \right)}^{-x}}\times {{\left( \sqrt{\frac{a}{b}} \right)}^{-y}}\times {{\left( \sqrt{\frac{a}{b}} \right)}^{-z}} \right]=\]______
A)
\[{{\left[ {{a}^{3}}/{{b}^{3}} \right]}^{x+y+z}}\] done
clear
B)
\[{{\left[ {{a}^{2}}/{{b}^{2}} \right]}^{x+y+z}}\] done
clear
C)
\[{{\left[ a/b \right]}^{\left( x+y+z \right)/2}}\] done
clear
D)
\[{{\left[ a/b \right]}^{3\left( x+y+z \right)/2}}\] done
clear
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question_answer22)
If \[{{\left( \mathbf{x}+\mathbf{y} \right)}^{\mathbf{3}}}=\mathbf{1331}\] and\[{{\left( \mathbf{x}-\mathbf{y} \right)}^{\mathbf{5}}}=\mathbf{243}\], then find \[{{\mathbf{x}}^{\mathbf{2}}}-{{\mathbf{y}}^{\mathbf{2}}}.\]
A)
33 done
clear
B)
22 done
clear
C)
11 done
clear
D)
44 done
clear
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question_answer23)
If xyz = 0, then find the value of \[{{({{a}^{x}})}^{zy}}+{{({{a}^{y}})}^{zx}}+{{({{a}^{z}})}^{xy}}\]
A)
3 done
clear
B)
2 done
clear
C)
1 done
clear
D)
0 done
clear
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question_answer24)
If \[{{\mathbf{2}}^{\mathbf{2}n-}}^{\mathbf{3}}=\mathbf{2048}\], then \[\left( 4n+3{{n}^{2}} \right)=\]________
A)
175 done
clear
B)
25 done
clear
C)
125 done
clear
D)
75 done
clear
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question_answer25)
Find the value of\[\frac{1}{1+{{x}^{a-b}}}+\frac{1}{1+{{x}^{b-a}}}\]
A)
0 done
clear
B)
\[-\]1 done
clear
C)
1 done
clear
D)
\[{{x}^{a+b}}\] done
clear
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question_answer26)
If \[{{2}^{2x-y}}=32\] and \[{{2}^{x+y}}=16\] then find \[{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}\]is equal to
A)
9 done
clear
B)
10 done
clear
C)
11 done
clear
D)
13 done
clear
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question_answer27)
\[{{\left( -9 \right)}^{3}}\div {{\left( -9 \right)}^{8}}\] is equal to
A)
(9)5 done
clear
B)
\[{{\left( 9 \right)}^{-5}}\] done
clear
C)
\[{{\left( -9 \right)}^{5}}\] done
clear
D)
\[{{\left( -9 \right)}^{-5}}\] done
clear
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question_answer28)
For any two non-zero rational numbers x and \[y,{{x}^{4}}\div {{y}^{4}}\]is equal to
A)
\[{{(x\div y)}^{0}}\] done
clear
B)
\[{{(x\div y)}^{1}}\] done
clear
C)
\[{{(x\div y)}^{4}}\] done
clear
D)
\[{{(x\div y)}^{8}}\] done
clear
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question_answer29)
\[{{\left[ {{\left( \frac{2}{13} \right)}^{-6}}\div {{\left( \frac{2}{13} \right)}^{3}} \right]}^{3}}\times {{\left( \frac{2}{13} \right)}^{-9}}\]
A)
\[{{\left( \frac{2}{13} \right)}^{36}}\] done
clear
B)
\[{{\left( \frac{2}{13} \right)}^{-36}}\] done
clear
C)
\[{{\left( \frac{2}{13} \right)}^{-36}}\] done
clear
D)
\[{{\left( \frac{2}{13} \right)}^{-36}}\] done
clear
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question_answer30)
Find the value of n if \[\frac{{{2}^{n}}\times {{2}^{6}}}{{{2}^{-3}}}={{2}^{18}}\]
A)
7 done
clear
B)
8 done
clear
C)
9 done
clear
D)
10 done
clear
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question_answer31)
Solve \[{{81}^{2x}}={{\left( 729 \right)}^{2}}\]
A)
\[x=\frac{3}{4}\] done
clear
B)
\[x=\frac{2}{3}\] done
clear
C)
\[x=\frac{5}{6}\] done
clear
D)
\[x=\frac{3}{2}\] done
clear
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question_answer32)
Which of the following has the same value of \[{{\mathbf{3}}^{6}}\times {{\left( {{\mathbf{3}}^{-\mathbf{2}}} \right)}^{2}}\times {{\left( {{\mathbf{2}}^{\mathbf{3}}} \right)}^{2}}\times {{\left( {{\mathbf{2}}^{-\mathbf{2}}} \right)}^{\mathbf{3}}}\]
A)
\[{{9}^{{}^\circ }}\] done
clear
B)
9 done
clear
C)
\[{{9}^{2}}\] done
clear
D)
\[{{9}^{3}}\] done
clear
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question_answer33)
The value of x so that \[{{\left( \frac{2}{7} \right)}^{4}}.{{\left( \frac{2}{7} \right)}^{3}}={{\left( \frac{2}{7} \right)}^{4x-1}}\] is
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
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question_answer34)
Avogadro number is written as 602,000,000,000,000,000,000,000, Express this number in standard form.
A)
\[6.02\times {{10}^{23}}\] done
clear
B)
\[6.02\times {{10}^{21}}\] done
clear
C)
\[602.0\times {{10}^{21}}\] done
clear
D)
\[0.602\times {{10}^{23}}\] done
clear
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question_answer35)
What is the simplified form of \[{{\left( -6xy \right)}^{6}}\div {{\left( -6xy \right)}^{2}}?\]
A)
\[{{\left( -6xy \right)}^{6}}\] done
clear
B)
\[{{\left( -6xy \right)}^{8}}\] done
clear
C)
\[\left( -\,6xy \right)\] done
clear
D)
\[{{\left( -6xy \right)}^{4}}\] done
clear
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question_answer36)
A number in standard form in written as \[\mathbf{6}.\mathbf{6}\times \mathbf{1}{{\mathbf{0}}^{\mathbf{6}}}.\] It can also be written as:
A)
6666666 done
clear
B)
66000 done
clear
C)
6600000000 done
clear
D)
6600000 done
clear
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question_answer37)
The speed of light is 300,000,000 \[\mathbf{m}{{\mathbf{s}}^{-1}}\] Express it in standard form.
A)
\[3.0\times {{10}^{8}}m{{s}^{-1}}\] done
clear
B)
\[3.0\times {{10}^{10}}m{{s}^{-1}}\] done
clear
C)
\[3.0\times {{10}^{6}}m{{s}^{-1}}\] done
clear
D)
\[3.0\times {{10}^{12}}m{{s}^{-1}}\] done
clear
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question_answer38)
Which is greater \[{{4}^{3}}\] or \[{{3}^{4}}\]?
A)
Both are equal done
clear
B)
\[{{4}^{3}}\] done
clear
C)
\[{{3}^{4}}\] done
clear
D)
cannot be determined done
clear
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question_answer39)
Solve \[{{\left( {{4}^{5}} \right)}^{x}}={{\left( {{4}^{4}} \right)}^{x}}\div {{4}^{2}}\]
A)
\[x=4\] done
clear
B)
\[x=-2\] done
clear
C)
\[x=-3\] done
clear
D)
\[x=2\] done
clear
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question_answer40)
The value of \[\frac{{{x}^{-4}}\times {{y}^{-6}}}{{{x}^{-16}}\times {{y}^{-7}}}\]
A)
\[{{x}^{-1}}\times {{y}^{-1}}\] done
clear
B)
\[{{x}^{-1}}{{y}^{-1}}\] done
clear
C)
\[\frac{1}{{{x}^{12}}y}\] done
clear
D)
\[{{x}^{12}}y\] done
clear
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