question_answer

Simplify and express each of the following as exponential form:

(a) \[{{2}^{\circ }}\times {{3}^{\circ }}\times {{4}^{\circ }}\]

(b)\[\left( 3{}^\circ \text{ }+\text{ }2{}^\circ  \right)\text{ }\times \text{ }5{}^\circ \]

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

Answer:

(a) \[{{2}^{0}}\times {{3}^{0}}\times {{4}^{0}}=1\times 1\times 1=1\]

(b) \[\left( {{3}^{0}}+{{2}^{0}} \right)\times {{5}^{0}}=\left( 1+1 \right)\times 1\]

= 2 × 1 = 2

(c)\[\frac{{{2}^{8}}\times {{a}^{5}}}{{{4}^{3}}\times {{a}^{3}}}=\frac{{{2}^{8}}\times {{a}^{5}}}{{{\left( {{2}^{2}} \right)}^{3}}\times {{a}^{3}}}=\frac{{{2}^{8}}\times {{a}^{5}}}{{{2}^{6}}\times {{a}^{3}}}\]

\[={{2}^{86}}\times {{a}^{53}}\]

\[={{2}^{2}}\times {{a}^{2}}={{\left( 2a \right)}^{2}}\]