| The value of \[\frac{{{(625)}^{6.25}}\times {{(25)}^{2.6}}}{{{(625)}^{6.75}}\times {{(5)}^{1.2}}}\]is |
A) 25
B) 30
C) 32
D) 33
Correct Answer: A
Solution :
| \[\frac{{{(625)}^{6.25}}\times {{(25)}^{2.6}}}{{{(625)}^{6.75}}\times {{(5)}^{1.2}}}\] |
| \[=[{{(625)}^{6.25}}\div {{(625)}^{6.75}}]\times {{({{5}^{2}})}^{2.6}}\div {{(5)}^{1.2}}]\] |
| \[=[{{(625)}^{6.25\,\,-\,\,6.75}}\times {{(5)}^{5.2-1.2}}\] |
| \[={{(625)}^{-\,\,0.50}}\times {{(5)}^{4}}\] |
| \[={{({{5}^{4}})}^{-\,\,0.5}}\times {{5}^{4}}\] |
| \[={{5}^{-\,\,2}}\times {{5}^{4}}={{5}^{2}}=25\] |
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