A) \[{{3}^{a-2}}{{.2}^{a-5}}{{.5}^{a+4}}\]
B) \[{{2}^{a-5}}{{.3}^{a+2}}{{.5}^{a+4}}\]
C) \[{{2}^{a+5}}{{.3}^{a+2}}{{.5}^{a+4}}\]
D) \[{{2}^{a-5}}{{.3}^{-a22}}{{.5}^{a+4}}\]
Correct Answer: B
Solution :
\[\frac{{{3}^{a}}.{{({{2}^{2}})}^{a-2}}.{{({{5}^{2}})}^{a+1}}}{{{({{3}^{2}})}^{a-1}}{{.2}^{a+1}}{{.5}^{a-2}}}\] \[=\frac{{{3}^{a}}{{.2}^{2a-4}}{{.5}^{2a+2}}}{{{3}^{2a-2}}{{.2}^{a+1}}{{.5}^{a-2}}}\] [Since\[{{({{a}^{m}})}^{n}}={{a}^{mn}}\].] \[={{3}^{a-2a+2}}{{.2}^{2a-4-a-1}}{{.5}^{2a+2-a+2}}\] Since \[\left[ \frac{{{a}^{m}}}{{{b}^{n}}}={{a}^{m-n}} \right]\] \[={{3}^{-a+2}}{{.2}^{a-5}}{{.5}^{a+4}}\] \[={{2}^{a-5}}{{.3}^{-a+2}}{{.5}^{a+4}}\]
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