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question_answer1)
What is the value of \[({{3}^{0}}-{{4}^{0}})\times {{5}^{2}}\]?
A)
\[25\] done
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B)
\[0\] done
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C)
\[-25\] done
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D)
\[1\] done
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question_answer2)
What is the value of \[{{\left( \frac{16}{81} \right)}^{2}}\]?
A)
\[\frac{9}{2}\] done
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B)
\[\frac{2}{9}\] done
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C)
\[{{\left( \frac{2}{3} \right)}^{8}}\] done
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D)
\[\frac{27}{8}\] done
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question_answer3)
Which of the following is true?
A)
\[10\times {{10}^{11}}={{100}^{11}}\] done
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B)
\[{{2}^{3}}\times {{3}^{2}}={{6}^{5}}\] done
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C)
\[{{2}^{3}}>{{3}^{2}}\] done
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D)
\[{{p}^{0}}={{1000}^{0}}\] done
clear
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question_answer4)
What is the value of \[(12\times {{3}^{0}}-8\times {{5}^{0}})\]?
A)
\[\frac{1}{2}\] done
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B)
\[2\] done
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C)
\[4\] done
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D)
\[\frac{1}{4}\] done
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question_answer5)
A Find the value of \[{{2}^{0}}+{{3}^{0}}+{{4}^{0}}\].
A)
\[3\] done
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B)
\[234\] done
clear
C)
\[1\] done
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D)
\[24\] done
clear
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question_answer6)
What is the value of \[{{2}^{7}}\times {{5}^{3}}\]?
A)
\[7500\] done
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B)
\[16000\] done
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C)
\[11200\] done
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D)
\[14000\] done
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question_answer7)
Which of the following is the least?
\[{{(-1)}^{3}},\,{{(-10)}^{3}},{{(1)}^{5}}\] and \[{{(-1)}^{4}}\] |
A)
\[{{1}^{5}}\] done
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B)
\[{{(-10)}^{3}}\] done
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C)
\[{{(-1)}^{4}}\] done
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D)
\[{{(-1)}^{3}}\] done
clear
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question_answer8)
Write \[a\times a\times a\times c\times c\times c\times c\times d\times d\] in exponential form.
A)
\[{{a}^{3}}{{c}^{3}}{{d}^{3}}\] done
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B)
\[{{a}^{3}}{{c}^{3}}d\] done
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C)
\[{{a}^{3}}{{c}^{3}}{{d}^{2}}\] done
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D)
\[{{a}^{3}}{{c}^{4}}{{d}^{2}}\] done
clear
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question_answer9)
\[{{(-11)}^{2}}\times {{(-11)}^{4}}={{(-11)}^{x}}.\]What is the value of x?
A)
\[2\] done
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B)
\[4\] done
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C)
\[6\] done
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D)
\[-2\] done
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question_answer10)
Which of the following statements is correct?
A)
\[{{({{2}^{3}})}^{2}}\] and \[{{({{3}^{2}})}^{4}}\] are not the same. done
clear
B)
\[{{({{2}^{3}})}^{2}}\] and \[{{({{3}^{4}})}^{2}}\] are the same. done
clear
C)
\[{{({{7}^{50}})}^{2}}={{7}^{502}}\] done
clear
D)
\[{{({{5}^{7}})}^{3}}={{5}^{73}}\] done
clear
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question_answer11)
Evaluate \[{{\left( \frac{5}{6} \right)}^{5}}\] .
A)
\[{{\left( \frac{6}{5} \right)}^{5}}\] done
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B)
\[{{({{5}^{6}})}^{5}}\] done
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C)
\[\frac{{{5}^{5}}}{{{6}^{5}}}\] done
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D)
\[{{({{5}^{5}})}^{6}}\] done
clear
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question_answer12)
Which of the following values are equal?
(i) \[{{1}^{4}}\] (ii) \[{{4}^{0}}\] (iii) \[{{0}^{4}}\] (iv) \[{{4}^{1}}\] |
A)
(i) and (ii) done
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B)
(ii) and (iii) done
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C)
(i) and (iii) done
clear
D)
(i) and (iv) done
clear
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question_answer13)
What is the sum of the powers of the prime factors in \[108\times 192\]?
A)
\[5\] done
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B)
\[7\] done
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C)
\[8\] done
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D)
\[12\] done
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question_answer14)
Express \[{{(-2)}^{3}}\div {{m}^{3}}\] in the form \[{{\left( \frac{a}{b} \right)}^{m}}\].
A)
\[\frac{-{{2}^{3}}}{{{m}^{3}}}\] done
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B)
\[{{\left( -\frac{2}{m} \right)}^{3}}\] done
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C)
\[\frac{{{(-2)}^{3}}}{{{m}^{3}}}\] done
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D)
\[-\left( \frac{2}{m} \right)\left( \frac{-2}{m} \right)\] done
clear
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question_answer15)
What is the value of \[\left[ {{\left( \frac{1}{4} \right)}^{2}}-{{\left( \frac{1}{4} \right)}^{2}} \right]\times {{2}^{6}}\]?
A)
\[1\] done
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B)
\[2\] done
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C)
\[3\] done
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D)
\[4\] done
clear
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question_answer16)
What is the result of \[\frac{2\times {{3}^{4}}\times {{2}^{5}}}{9\times {{4}^{2}}}\]?
A)
\[36\] done
clear
B)
\[42\] done
clear
C)
\[46\] done
clear
D)
\[48\] done
clear
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question_answer17)
Express \[\frac{729\times 64}{270}\] as a product of prime factors in exponential form.
A)
\[{{2}^{5}}\times {{3}^{4}}\] done
clear
B)
\[\frac{{{2}^{5}}\times {{3}^{3}}}{5}\] done
clear
C)
\[\frac{{{2}^{6}}\times {{3}^{3}}}{{{5}^{3}}}\] done
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D)
\[\frac{{{2}^{6}}\times {{3}^{3}}}{{{5}^{2}}}\] done
clear
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question_answer18)
How is 65950 expressed in standard form?
A)
\[6.59\text{ }x{{10}^{6}}\] done
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B)
\[6.595\text{ }x{{10}^{5}}\] done
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C)
\[6.595\text{ }x{{10}^{4}}\] done
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D)
\[6.59\text{ }x{{10}^{5}}\] done
clear
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question_answer19)
Express 15625 as a power of 5.
A)
\[{{5}^{6}}\] done
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B)
\[{{5}^{4}}\] done
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C)
\[{{5}^{8}}\] done
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D)
\[{{5}^{7}}\] done
clear
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question_answer20)
Find the value of \[{{16}^{\frac{3}{4}}}\times {{4}^{\frac{-1}{2}}}.\]
A)
\[8\] done
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B)
\[1\] done
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C)
4 done
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D)
\[0\] done
clear
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question_answer21)
Find the numerical value of \[{{(4096)}^{\frac{-3}{4}}}\].
A)
\[1024\] done
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B)
\[512\] done
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C)
\[256\] done
clear
D)
\[\frac{1}{512}\] done
clear
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question_answer22)
Simplify \[\frac{{{(9{{m}^{2}})}^{1/3}}}{{{6}^{4}}}\times \frac{{{(4{{n}^{2}})}^{1/3}}}{5m}\].
A)
\[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{1/3}}\] done
clear
B)
\[\frac{1}{5}{{\left[ \frac{n}{{{m}^{2}}{{6}^{10}}} \right]}^{1/3}}\] done
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C)
\[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{-10}}} \right]}^{1/3}}\] done
clear
D)
\[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{2/3}}\] done
clear
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question_answer23)
Solve \[{{9}^{4x}}\div {{3}^{2x}}=2187\].
A)
\[x=\frac{6}{7}\] done
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B)
\[x=\frac{-7}{6}\] done
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C)
\[x=\frac{7}{6}\] done
clear
D)
\[x=\frac{-6}{7}\] done
clear
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question_answer24)
Simplify and leave the answer in exponent form.
\[{{\left( \frac{6}{7} \right)}^{-2}}\times {{\left( \frac{7}{6} \right)}^{-2}}\] |
A)
\[\frac{7}{6}\] done
clear
B)
\[1\] done
clear
C)
\[\frac{-6}{7}\] done
clear
D)
\[\frac{6}{7}\] done
clear
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question_answer25)
Simplify \[\frac{{{p}^{4}}{{q}^{3}}\times {{p}^{2}}{{r}^{4}}\times {{q}^{-2}}\times {{r}^{3}}}{{{p}^{-3}}{{q}^{3}}{{r}^{3}}}\].
A)
\[{{p}^{3}}{{q}^{4}}{{r}^{7}}\] done
clear
B)
\[{{p}^{3}}{{q}^{4}}{{r}^{10}}\] done
clear
C)
\[{{p}^{-9}}{{q}^{2}}{{r}^{-4}}\] done
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D)
\[{{p}^{9}}{{q}^{-2}}{{r}^{4}}\] done
clear
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question_answer26)
Find the numerical value of \[{{256}^{0.75}}\].
A)
\[64\] done
clear
B)
\[256\] done
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C)
\[1\] done
clear
D)
\[{{4}^{-3}}\] done
clear
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question_answer27)
Simplify \[\frac{{{({{a}^{-n}})}^{m}}\times {{a}^{-2m}}}{{{a}^{mn}}\times {{a}^{2m}}}\].
A)
\[{{a}^{2m(n-2)}}\] done
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B)
\[{{a}^{2m(2n-4)}}\] done
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C)
\[{{a}^{-2m(n+2)}}\] done
clear
D)
\[{{a}^{2m(n-4)}}\] done
clear
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question_answer28)
Simplify \[\frac{{{(16{{a}^{2}})}^{\frac{1}{2}}}\times {{(36\,{{a}^{4}})}^{\frac{-1}{2}}}}{2{{a}^{\frac{1}{2}}}\times 5{{a}^{\frac{3}{2}}}\times 8{{a}^{\frac{9}{4}}}}\].
A)
\[120\,\,{{a}^{\frac{25}{4}}}\] done
clear
B)
\[\frac{1}{120\,{{a}^{\frac{25}{4}}}}\] done
clear
C)
\[24{{a}^{\frac{-25}{4}}}\] done
clear
D)
\[24{{a}^{\frac{25}{4}}}\] done
clear
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question_answer29)
Express \[{{6}^{2}}\times {{7}^{-4}}\times {{({{8}^{-2}})}^{2}}\times {{6}^{3}}\times {{7}^{2}}\times {{8}^{4}}\] in the simplest exponential form.
A)
\[{{6}^{5}}\,{{7}^{2}}\] done
clear
B)
\[\frac{{{6}^{5}}}{{{7}^{2}}}\] done
clear
C)
\[{{6}^{-5}}\,{{7}^{2}}\] done
clear
D)
\[{{6}^{-5}}\,{{7}^{-2}}\] done
clear
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question_answer30)
Solve \[{{9}^{2x}}=729.\]
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_answer31)
Find the value of x.
\[{{({{5}^{3}})}^{x}}\times {{({{5}^{8}})}^{x}}={{5}^{72}}\] |
A)
\[x=6\frac{6}{11}\] done
clear
B)
\[x=9\] done
clear
C)
\[x=6\] done
clear
D)
\[x=8\] done
clear
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question_answer32)
Simplify \[\frac{a{{b}^{2}}{{c}^{3}}\times {{a}^{4}}{{b}^{5}}{{c}^{-5}}}{{{a}^{-7}}{{b}^{-8}}{{c}^{9}}\times {{a}^{10}}{{b}^{11}}{{c}^{-12}}\times {{a}^{13}}{{b}^{-14}}{{c}^{15}}}\].
A)
\[{{a}^{11}}{{b}^{18}}{{c}^{-15}}\] done
clear
B)
\[{{a}^{11}}{{b}^{18}}{{c}^{15}}\] done
clear
C)
\[{{a}^{-11}}{{b}^{-18}}{{c}^{15}}\] done
clear
D)
\[{{a}^{-11}}{{b}^{18}}{{c}^{-15}}\] done
clear
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question_answer33)
A The mass of the Earth is 5,976,000,000, 000,000,000,000,000 kg. How is the mass of Earth expressed in standard form?
A)
\[5.976\times {{10}^{24}}\,kg\] done
clear
B)
\[5.976\times {{10}^{21}}\,kg\] done
clear
C)
\[5976\times {{10}^{21}}\,kg\] done
clear
D)
\[59.76\times {{10}^{23}}\,kg\] done
clear
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question_answer34)
What is the simplified form of \[{{(-5xy)}^{4}}\div {{(-5xy)}^{2}}\]?
A)
\[{{(-5xy)}^{6}}\] done
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B)
\[{{(-5xy)}^{8}}\] done
clear
C)
\[{{(-5xy)}^{4}}\] done
clear
D)
\[{{(-5xy)}^{2}}\] done
clear
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question_answer35)
Which of the following equals \[(-1)\]?
A)
\[{{(3-2)}^{235}}\] done
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B)
\[{{(-1)}^{47}}\] done
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C)
Both [a] and [b] done
clear
D)
Neither [a] nor [b] done
clear
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question_answer36)
What is the simplified form of the product given?
\[{{(-3p)}^{4}}{{(6q)}^{5}}{{(3r)}^{6}}\] |
A)
\[{{(-3)}^{15}}{{2}^{5}}{{p}^{4}}{{q}^{5}}{{r}^{6}}\] done
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B)
\[{{p}^{4}}\,{{q}^{5}}\,{{r}^{6}}\] done
clear
C)
\[{{3}^{15}}\,{{2}^{5}}\,{{p}^{4}}\,{{q}^{5}}\,{{r}^{6}}\] done
clear
D)
\[{{(-3)}^{15}}\,{{2}^{5}}\,{{p}^{4}}\,{{q}^{4}}\,{{r}^{4}}\] done
clear
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question_answer37)
The speed of light in vacuum is\[300,\text{ }000,\text{ }000\text{ }m{{s}^{-1}}\]. 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
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C)
\[3.0\times {{10}^{6}}\,m{{s}^{-1}}\] done
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D)
\[3.0\times {{10}^{12}}\,m{{s}^{-1}}\] done
clear
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question_answer38)
Which is greater \[{{2}^{3}}\] or \[{{5}^{2}}\]?
A)
Both are equal. done
clear
B)
\[{{2}^{3}}\] done
clear
C)
\[{{5}^{2}}\] done
clear
D)
Cannot be determined. done
clear
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question_answer39)
Solve \[{{({{9}^{5}})}^{x}}={{({{9}^{4}})}^{x}}\div {{9}^{2}}\].
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)
Simplify \[\frac{{{64}^{2x}}\div {{16}^{x}}}{{{128}^{x}}\times {{4}^{2x}}}\].
A)
\[{{2}^{-3x}}\] done
clear
B)
\[{{2}^{8x}}\] done
clear
C)
\[{{2}^{3x}}\] done
clear
D)
\[{{2}^{11x}}\] done
clear
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