Find the value of : (i) \[{{2}^{6}}\] (ii) \[{{9}^{3}}\] (iii) \[{{11}^{2}}\] (iv) \[{{5}^{4}}\]
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Express the following in exponential form: (i) \[6\times 6\times 6\times 6\] (ii) \[t\times t\] (iii) \[b\times b\times b\times b\] (iv) \[5\times 5\times 7\times 7\times 7\] (v) \[2\times 2\times a\times a\] (vi) \[a\times a\times a\times c\times c\times c\times c\times d\]
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Express each of the following numbers using exponential notation:
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Identify the greater number, wherever possible, in each of the following? (i) \[{{4}^{3}}\]or \[{{3}^{4}}\] (ii) \[{{5}^{3}}\]or \[{{3}^{5}}\] (iii) \[{{2}^{8}}\]or \[{{8}^{2}}\] (iv) \[{{100}^{2}}\]or \[{{2}^{100}}\]
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Express each of the following as product of powers of their prime factors: (i) 648 (ii) 405 (iii) 540 (iv) 3600.
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Simplify: (i) \[2\times {{10}^{3}}\] (ii) \[{{7}^{2}}\times {{2}^{2}}\] (iii) \[{{2}^{3}}\times 5\] (iv) \[3\times {{4}^{4}}\] (v) \[0\times {{10}^{2}}\] (vi) \[{{5}^{2}}\times {{3}^{3}}\] (vii) \[{{2}^{4}}\times {{3}^{2}}\] (viii) \[{{3}^{2}}\times {{10}^{4}}\]
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Simplify : (i) \[{{(-4)}^{3}}\] (ii) \[(-3)\times {{(-2)}^{3}}\] (iii) \[{{(-3)}^{2}}\times {{(-5)}^{2}}\] (iv) \[{{(-2)}^{3}}\times {{(-10)}^{3}}\]
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Compare the following numbers: (i) \[2.7\times {{10}^{12}};1.5\times {{10}^{8}}\] (ii) \[4\times {{10}^{14}};3\times {{10}^{17}}\]
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Using laws of exponents, simplify and write the answer in exponential form: (i) \[{{3}^{2}}\times {{3}^{4}}\times {{3}^{8}}\] (ii) \[{{6}^{15}}\div {{6}^{10}}\] (iii) \[{{a}^{3}}\times {{a}^{2}}\] (iv) \[{{7}^{x}}\times {{7}^{2}}\] (v) \[{{({{5}^{2}})}^{3}}\div {{5}^{3}}\] (vi) \[{{2}^{5}}\times {{5}^{5}}\] (vii) \[{{a}^{4}}\times {{b}^{4}}\] (viii) \[{{({{3}^{4}})}^{3}}\] (ix) \[({{2}^{20}}\div {{2}^{15}})\times {{2}^{3}}\]
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Simplify the express each of the following as exponent: (i) \[\frac{{{2}^{3}}\times {{3}^{4}}\times 4}{3\times 32}\] (ii) \[\left( ({{5}^{2}})\times {{5}^{4}} \right)\div {{5}^{7}}\] (iii) \[{{25}^{4}}\div {{5}^{3}}\] (iv) \[\frac{3\times {{7}^{2}}\times {{11}^{8}}}{21\times {{11}^{3}}}\] (v) \[\frac{{{3}^{7}}}{{{3}^{4}}\times {{3}^{3}}}\] (vi) \[{{2}^{0}}+{{3}^{0}}+{{4}^{0}}\] (vii) \[{{2}^{0}}\times {{3}^{0}}\times {{4}^{0}}\] (viii) \[({{3}^{0}}+{{2}^{0}})\times {{5}^{0}}\] (ix) \[\frac{{{2}^{8}}\times {{a}^{5}}}{{{4}^{3}}\times {{a}^{3}}}\] (x) \[\left( \frac{{{a}^{5}}}{{{a}^{3}}} \right)\times {{a}^{8}}\] (xi) \[\frac{{{4}^{5}}\times {{a}^{8}}{{b}^{3}}}{{{4}^{5}}\times {{a}^{5}}{{b}^{2}}}\] (xii) \[{{({{2}^{3}}\times 2)}^{2}}\]
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Say true or false and justify your answer: (i) \[10\times {{10}^{11}}={{100}^{11}}\] (ii) \[{{2}^{3}}>{{5}^{2}}\] (iii) \[{{2}^{3}}\times {{3}^{2}}={{6}^{5}}\] (iv) \[{{3}^{0}}={{(1000)}^{0}}\].
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Express each of the following as a product of prime factors only in exponential form: (i) \[108\times 192\] (ii) \[\text{27}0\] (iii) \[729\times 64\] (iv) \[768\]
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Simplify (i) \[\frac{{{({{2}^{5}})}^{2}}\times {{7}^{3}}}{{{8}^{3}}\times 7}\] (ii) \[\frac{25\times {{5}^{2}}\times {{t}^{8}}}{{{10}^{3}}\times {{t}^{4}}}\] (iii) \[\frac{{{3}^{5}}\times {{10}^{5}}\times 25}{{{5}^{7}}\times {{6}^{5}}}\]
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Write the following numbers in the expand forms: (i) 279404, (ii) 3006194, (iii) 2806196, (iv) 120719,
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Find the number from each of the following expanded forms: (a) \[8\times {{10}^{4}}+6\times {{10}^{3}}+0\times {{10}^{2}}+4\times {{10}^{1}}+5\times {{10}^{0}}\] (b) \[4\times {{10}^{5}}+5\times {{10}^{3}}+3\times {{10}^{2}}+2\times {{10}^{0}}\] (c) \[3\times {{10}^{4}}+7\times {{10}^{2}}+5\times {{10}^{0}}\] (d) \[9\times {{10}^{5}}+2\times {{10}^{2}}+3\times {{10}^{1}}\]
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Express the following number in standard form: (i) \[5,00,00,000\] (ii) \[70,00,000\] (iii) \[3,18,65,00,000\] (iv) \[3,90,878\] (v) \[39087.8\] (vi) \[3908.78\]
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Express the number appearing in the following statements in standard form: (a) The distance between Earth and Moon is \[384,000,000m\] (b) Speed of light in vacuum is \[300,000,000m/s\] (c) Diameter of the Earth is \[1,27,56,000m\]. (d) Diameter of the sun is \[1,400,000,000m\] (e) In a galaxy here are on an average \[100,000,000,000\]stars. (f) The universe is estimated to be about \[12,000,000,000\]years old. (g)The distance of Sun from the centre of the Milky Way Galaxy is estimated to be \[300,000,000,000,000,000,000m\] (h)\[60,230,000,000,000,000,000,000\]molecules are contained in a drop of water weighing \[1.8gm.\] (i) The earth has \[1,353,000,000\]cubic km of sea water. (j) The population of India was about \[1,027,000,000\]in March, 2001.
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