question_answer

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) \[{{2}^{0}}+{{3}^{0}}+{{4}^{0}}=1+1+1=3\]