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question_answer1)
What is the value of \[({{3}^{0}}-{{4}^{0}})\times {{5}^{-3}}\]?
A)
\[25\] done
clear
B)
\[0\] done
clear
C)
\[-25\] done
clear
D)
\[-125\] done
clear
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question_answer2)
What is the solution of \[{{3}^{3x-5}}=\frac{1}{{{9}^{x}}}\]?
A)
\[\frac{5}{2}\] done
clear
B)
\[5\] done
clear
C)
\[1\] done
clear
D)
\[\frac{7}{3}\] done
clear
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question_answer3)
Find the value of \[{{\left[ {{(-3)}^{(-2)}} \right]}^{(-3)}}\].
A)
\[729\] done
clear
B)
\[32\] done
clear
C)
\[64\] done
clear
D)
\[-729\] done
clear
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question_answer4)
Evaluate: \[{{\left( \frac{16}{81} \right)}^{\frac{3}{4}}}\]
A)
\[\frac{9}{2}\] done
clear
B)
\[\frac{2}{9}\] done
clear
C)
\[\frac{8}{27}\] done
clear
D)
\[\frac{27}{8}\] done
clear
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question_answer5)
What is the value of \[{{(512)}^{\frac{-2}{9}}}\]?
A)
\[\frac{1}{2}\] done
clear
B)
\[2\] done
clear
C)
\[4\] done
clear
D)
\[\frac{1}{4}\] done
clear
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question_answer6)
Simplify \[{{(32)}^{\frac{-2}{5}}}\div {{(125)}^{\frac{-2}{3}}}\].
A)
\[\frac{4}{25}\] done
clear
B)
\[\frac{25}{4}\] done
clear
C)
\[\frac{2}{5}\] done
clear
D)
\[\frac{5}{2}\] done
clear
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question_answer7)
If \[{{x}^{y}}={{y}^{x}},\]find the value of \[{{\left( \frac{x}{y} \right)}^{\frac{x}{y}}}\].
A)
\[{{x}^{\frac{x}{y}}}\] done
clear
B)
\[{{x}^{\frac{x}{y}-1}}\] done
clear
C)
\[{{x}^{\frac{y}{x}}}\] done
clear
D)
\[{{x}^{\frac{y}{x}-1}}\] done
clear
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question_answer8)
Evaluate \[\frac{{{(5)}^{0.25}}\times {{(125)}^{0.25}}}{{{(256)}^{0.10}}\times {{(256)}^{0.15}}}\].
A)
\[\frac{\sqrt{5}}{2}\] done
clear
B)
\[\frac{5}{4}\] done
clear
C)
\[\frac{25}{2}\] done
clear
D)
\[\frac{25}{16}\] done
clear
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question_answer9)
What is the value of \[\frac{{{(67.542)}^{2}}-{{(32.458)}^{2}}}{75.458-40.374}\]?
A)
\[1\] done
clear
B)
\[10\] done
clear
C)
\[100\] done
clear
D)
\[-10\] done
clear
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question_answer10)
Which of the following values are equal?
I. | \[{{1}^{4}}\] |
II. | \[{{4}^{0}}\] |
III. | \[{{0}^{4}}\] |
IV. | \[{{4}^{1}}\] |
A)
I and II done
clear
B)
II and III done
clear
C)
I and III done
clear
D)
I and IV done
clear
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question_answer11)
Find the sum of the powers of the prime factors in\[108\times 192\].
A)
\[5\] done
clear
B)
\[7\] done
clear
C)
\[8\] done
clear
D)
\[12\] done
clear
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question_answer12)
Find the value of \[3\sqrt[3]{2}\times 7\sqrt[3]{6}\times 5\sqrt[3]{18}\]
A)
\[545\] done
clear
B)
\[500\] done
clear
C)
\[630\] done
clear
D)
\[360\] done
clear
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question_answer13)
Find the value of \[{{(-3)}^{0}}-{{(-3)}^{3}}-{{(-3)}^{-1}}+{{(-3)}^{4}}-{{(-3)}^{-2}}\].
A)
\[109\frac{2}{9}\] done
clear
B)
\[102\frac{2}{9}\] done
clear
C)
\[109\] done
clear
D)
\[110\] done
clear
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question_answer14)
Evaluate \[\frac{{{(-1)}^{13}}}{{{2}^{3}}}+\frac{{{2}^{3}}-{{1}^{10}}+{{3}^{2}}}{{{3}^{2}}-{{2}^{2}}}+{{\left( \frac{7}{11} \right)}^{3}}\div \frac{98}{121}\].
A)
\[3\frac{173}{440}\] done
clear
B)
\[3\frac{17}{44}\] done
clear
C)
\[3\frac{137}{440}\] done
clear
D)
\[3\frac{21}{440}\] done
clear
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question_answer15)
If \[{{(25)}^{{}}}={{(125)}^{y}},\]find \[x:y\].
A)
\[1:1\] done
clear
B)
\[2:3\] done
clear
C)
\[3:2\] done
clear
D)
\[1:3\] done
clear
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question_answer16)
Compute \[\frac{{{(64)}^{-1/6}}\times {{(216)}^{-1/3}}\times {{(81)}^{1/4}}}{{{(512)}^{-1/3}}\times {{(16)}^{1/4}}\times {{(9)}^{-1/2}}}\]
A)
\[3\] done
clear
B)
\[6\] done
clear
C)
\[1\] done
clear
D)
\[-6\] done
clear
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question_answer17)
What is the simplified form of \[\left[ \sqrt[3]{{{x}^{4}}y}\times \frac{1}{\sqrt[4]{{{x}^{2}}{{y}^{8}}}} \right]?\]
A)
\[{{x}^{5}}.{{y}^{10}}\] done
clear
B)
\[\frac{{{y}^{10}}}{{{x}^{5}}}\] done
clear
C)
\[\frac{{{y}^{2}}}{x}\] done
clear
D)
\[\frac{{{x}^{5}}}{{{y}^{5}}}\] done
clear
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question_answer18)
Find the value of \[\frac{1}{1+{{x}^{-m}}}+\frac{1}{1+{{x}^{m}}}.\]
A)
\[0\] done
clear
B)
\[{{x}^{m}}\] done
clear
C)
\[1\] done
clear
D)
\[{{x}^{-m}}\] done
clear
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question_answer19)
Give the simplified form of \[\frac{{{3}^{a}}{{4}^{a-2}}{{25}^{a+1}}}{{{9}^{a-1}}{{2}^{a+1}}{{5}^{a-2}}}\].
A)
\[{{3}^{a-2}}{{.2}^{a-5}}{{.5}^{a+4}}\] done
clear
B)
\[{{2}^{a-5}}{{.3}^{a+2}}{{.5}^{a+4}}\] done
clear
C)
\[{{2}^{a+5}}{{.3}^{a+2}}{{.5}^{a+4}}\] done
clear
D)
\[{{2}^{a-5}}{{.3}^{-a22}}{{.5}^{a+4}}\] done
clear
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question_answer20)
Which is greater of \[{{2}^{12}}\] and\[{{3}^{8}}\]?
A)
\[{{3}^{8}}\] done
clear
B)
\[{{2}^{12}}\] done
clear
C)
Both are equal. done
clear
D)
Cannot be compared. done
clear
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question_answer21)
What is the simplified form of \[\frac{{{\left( {{x}^{a+b}} \right)}^{3}}.{{\left( {{x}^{b+c}} \right)}^{3}}.{{\left( {{x}^{c+a}} \right)}^{3}}}{{{\left( {{x}^{a}}.{{x}^{b}}.{{x}^{c}} \right)}^{6}}}\]?
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[{{x}^{a+b+c}}\] done
clear
D)
\[x\] done
clear
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question_answer22)
If \[{{3}^{n}}=729,\] find the value of \[{{3}^{3n+1}}\].
A)
\[{{3}^{21}}\] done
clear
B)
\[{{3}^{10}}\] done
clear
C)
\[{{3}^{19}}\] done
clear
D)
\[{{3}^{15}}\] done
clear
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question_answer23)
If \[{{27}^{x+1}}={{9}^{x+3}}={{3}^{y}},\] find the respective values of ?x' and 'y'.
A)
3 and 12 done
clear
B)
12 and 3 done
clear
C)
6 and 6 done
clear
D)
4 and 9 done
clear
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question_answer24)
Find \[{{(0.000064)}^{5/4}}\times {{(0.04)}^{5/4}}\].
A)
\[{{2}^{10}}{{.10}^{10}}\] done
clear
B)
\[{{2}^{10}}{{.10}^{-10}}\] done
clear
C)
\[{{2}^{-10}}{{.10}^{10}}\] done
clear
D)
\[{{2}^{-10}}{{.10}^{-10}}\] done
clear
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question_answer25)
By what number should we multiply \[{{4}^{-3}}\]so that the product may be equal to 64?
A)
\[{{4}^{5}}\] done
clear
B)
\[{{2}^{12}}\] done
clear
C)
\[{{2}^{6}}\] done
clear
D)
\[1\] done
clear
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question_answer26)
What is the number to be multiplied by \[{{(-7)}^{-1}}\] so as to get \[{{10}^{-1}}\] as the product?
A)
\[\frac{-7}{10}\] done
clear
B)
\[\frac{7}{10}\] done
clear
C)
\[\frac{9}{10}\] done
clear
D)
\[\frac{-3}{10}\] done
clear
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question_answer27)
What is the value of \[({{6}^{-1}}-{{8}^{-1}})+{{({{2}^{-1}}-{{3}^{-1}})}^{-1}}\]?
A)
\[25\] done
clear
B)
\[30\] done
clear
C)
\[35\] done
clear
D)
\[40\] done
clear
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question_answer28)
What is the standard form of\[6020000000000000\]?
A)
\[6.02\times {{10}^{15}}\] done
clear
B)
\[6.02\times {{10}^{13}}\] done
clear
C)
\[602\times {{10}^{13}}\] done
clear
D)
\[602\times {{10}^{-15}}\] done
clear
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question_answer29)
What is the usual form of\[1.0001\times {{10}^{9}}\]?
A)
\[100010000\] done
clear
B)
\[1000100000\] done
clear
C)
\[10001000000000\] done
clear
D)
\[10001000000\] done
clear
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question_answer30)
The size of a plant cell is\[0.00001275\text{ }m\]. Express this size in standard form.
A)
\[1.25\times {{10}^{8}}m\] done
clear
B)
\[1.275\times {{10}^{5}}m\] done
clear
C)
\[1.275\times {{10}^{-8}}m\] done
clear
D)
\[1.275\times {{10}^{-5}}m\] done
clear
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question_answer31)
Evaluate \[{{\left\{ {{\left( \frac{3}{4} \right)}^{-1}}-{{\left( \frac{1}{4} \right)}^{-1}} \right\}}^{-1}}\].
A)
\[\frac{3}{16}\] done
clear
B)
\[\frac{-3}{8}\] done
clear
C)
\[\frac{16}{3}\] done
clear
D)
\[\frac{-8}{3}\] done
clear
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question_answer32)
A box has 5 books, each 20 mm thick and 5 cards each 0.016 mm thick. What is the total thickness?
A)
\[1.0008\times {{10}^{4}}mm\] done
clear
B)
\[1.008\times {{10}^{3}}mm\] done
clear
C)
\[1.0008\times {{10}^{2}}mm\] done
clear
D)
\[1.0008\times {{10}^{5}}mm\] done
clear
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question_answer33)
The size of a red blood cell is\[0.000007\text{ }m\] . The size of a plant cell is\[0.00001275\text{ }m\]. Compare them.
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{4}\] done
clear
C)
\[\frac{1}{5}\] done
clear
D)
\[-\frac{1}{5}\] done
clear
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question_answer34)
By what number should \[{{(-8)}^{-1}}\] be divided to get \[{{10}^{-1}}\]?
A)
\[\frac{4}{5}\] done
clear
B)
\[\frac{-5}{4}\] done
clear
C)
\[\frac{-4}{5}\] done
clear
D)
\[\frac{5}{4}\] done
clear
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question_answer35)
What is the value of \[{{\left( \frac{-1}{216} \right)}^{-2/3}}\]?
A)
\[36\] done
clear
B)
\[-36\] done
clear
C)
\[\frac{1}{36}\] done
clear
D)
\[\frac{-1}{36}\] done
clear
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question_answer36)
Evaluate: \[\frac{1}{{{(216)}^{-2/3}}}+\frac{1}{{{(256)}^{-3/4}}}+\frac{1}{{{(32)}^{-1/5}}}\].
A)
\[102\] done
clear
B)
\[105\] done
clear
C)
\[107\] done
clear
D)
\[109\] done
clear
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question_answer37)
How much is \[\left[ {{10}^{150}}\div {{10}^{146}} \right]\]?
A)
\[1000\] done
clear
B)
\[10000\] done
clear
C)
\[100000\] done
clear
D)
\[{{10}^{6}}\] done
clear
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question_answer38)
Evaluate the product \[{{5}^{1/4}}\times {{(125)}^{0.25}}\].
A)
\[\sqrt{5}\] done
clear
B)
\[5\] done
clear
C)
\[5\sqrt{5}\] done
clear
D)
\[25\] done
clear
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question_answer39)
How much is \[{{(0.04)}^{-1.5}}\]?
A)
\[25\] done
clear
B)
\[125\] done
clear
C)
\[250\] done
clear
D)
\[625\] done
clear
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question_answer40)
What is the value of \[\left( {{8}^{-25}}-{{8}^{-26}} \right)\] ?
A)
\[7\times {{8}^{-25}}\] done
clear
B)
\[8\times {{8}^{-26}}\] done
clear
C)
\[7\times {{8}^{-26}}\] done
clear
D)
\[8\times {{8}^{-25}}\] done
clear
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question_answer41)
If \[{{(25)}^{7.5}}\times {{(5)}^{2.5}}\div {{(125)}^{1.5}}={{5}^{x}},\] find 'x'.
A)
\[8.5\] done
clear
B)
\[13\] done
clear
C)
\[16\] done
clear
D)
\[17.5\] done
clear
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question_answer42)
What is the value of 'x' if \[\frac{{{a}^{x}}}{{{a}^{y}}}={{a}^{10}}\] and \[{{({{a}^{y}})}^{3}}={{a}^{x}}\] for \[a>1\]?
A)
\[25\] done
clear
B)
\[5\] done
clear
C)
\[20\] done
clear
D)
\[15\] done
clear
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question_answer43)
If \[x>0,\]which of the following is equal to \[\sqrt{{{x}^{3}}}\]?
(i) \[x+{{x}^{1/2}}\] |
(ii) \[{{({{x}^{\frac{1}{2}}})}^{3}}\] |
(iii) \[({{x}^{2}})\,{{(x)}^{\frac{-1}{2}}}\] |
A)
(ii) and (iii) only done
clear
B)
(i) and (ii) only done
clear
C)
(i) and (iii) only done
clear
D)
(i), (ii) and (iii) done
clear
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question_answer44)
If \[{{x}^{2}}=16\]and \[{{y}^{2}}=4,\]what is the greatest possible value of\[{{(x-y)}^{2}}\]?
A)
\[4\] done
clear
B)
\[-36\] done
clear
C)
\[-4\] done
clear
D)
\[36\] done
clear
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question_answer45)
If \[\sqrt{5}=x-2,\] what is the value of\[{{(x-2)}^{3}}\]?
A)
\[\sqrt{25}\] done
clear
B)
\[\sqrt{65}\] done
clear
C)
\[5\sqrt{5}\] done
clear
D)
\[2\sqrt{5}\] done
clear
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