Simplify and express each of the following as exponential form: |
(a) \[\frac{3\times {{7}^{2}}\times {{11}^{8}}}{21\times {{11}^{3}}}\] |
(b) \[\frac{{{3}^{7}}}{{{3}^{4}}\times {{3}^{3}}}\] |
(c) \[{{2}^{\circ }}+{{3}^{\circ }}+{{4}^{\circ }}\] |
Answer:
(a)\[\frac{3\times {{7}^{2}}\times {{11}^{8}}}{21\times {{11}^{3}}}=\frac{3\times {{7}^{2}}\times {{11}^{8}}}{3\times 7\times {{11}^{3}}}\] \[={{3}^{11}}\times {{7}^{21}}\times {{11}^{83}}\] \[=\text{ }30\times 71\times {{11}^{5}}\] \[=1\times 7\times {{11}^{5}}\] \[=7\times {{11}^{5}}\] (b)\[\frac{{{3}^{7}}}{{{3}^{4}}\times {{3}^{3}}}=\frac{{{3}^{7}}}{{{3}^{4+}}^{3}}=\frac{{{3}^{7}}}{{{3}^{7}}}\] (c) \[{{2}^{0}}+{{3}^{0}}+{{4}^{0}}=1+1+1=3\]
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