question_answer

Simplify and express each of the following as exponential form:

(a) \[\left( \frac{{{a}^{5}}}{{{a}^{3}}} \right)\times {{a}^{8}}\]

(b) \[\frac{{{4}^{5}}\times {{a}^{8}}{{b}^{3}}}{{{4}^{5}}\times {{a}^{5}}{{b}^{2}}}\]

(c) \[{{\left( {{2}^{3}}\times 2 \right)}^{2}}\]

Answer:

(a)        \[\left( \frac{{{a}^{5}}}{{{a}^{3}}} \right)\times {{a}^{8}}=({{a}^{5-3}})\times {{a}^{8}}\]

= \[{{a}^{2}}\times {{a}^{8}}={{a}^{2+8}}={{a}^{10}}\]

(b) \[\frac{{{4}^{5}}\times {{a}^{8}}{{b}^{3}}}{{{4}^{5}}\times {{a}^{5}}{{b}^{2}}}={{4}^{5-5}}\times {{a}^{8-5}}\times {{b}^{3-2}}\]

\[={{4}^{0}}\times {{a}^{3}}\times {{b}^{1}}\]

\[=\text{ }1\times {{a}^{3}}\times b={{a}^{3}}b\]

(c) \[{{\left( {{2}^{3}}\times 2 \right)}^{2}}={{\left( {{2}^{3}}+1 \right)}^{2}}={{\left( 24 \right)}^{2}}=28\]