Question

p please solve this problem in explanation​

Answer 1

Question

$\sf \large \dfrac{( { \frac{ - 3}{5} )}^{3} \times {( \frac{9}{25} )}^{2} \times { (\frac{ - 18}{125} )}^{0} }{ \frac{ - 27}{125} \times ( - \frac{3}{5}) }$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto\large \dfrac{( { \frac{ - 3}{5} )}^{3} \times {( \frac{9}{25} )}^{2} \times { (\frac{ - 18}{125} )}^{0} }{ \frac{ - 27}{125} \times ( - \frac{3}{5}) }$

$\sf \longmapsto\large \dfrac{( { \cancel{{ \frac{ - 3}{5} )}^{3}}} \times {( \frac{9}{25} )}^{2} \times { (\frac{ - 18}{125} )}^{0} }{ { \cancel{{(\frac{ -3}{5} )}^{3}}}\times ( - \frac{3}{5}) }$

$\sf \longmapsto \large\dfrac{ { (\frac{9}{25}) }^{2} \times {( \frac{ - 18}{125} )}^{0} }{( - \frac{3}{5}) }$

=>9 is the square of 3 & 25 is the square of 5

So, 9 can also be written as 3² and 25 can be written as 5².

$\sf \longmapsto \large\dfrac{( { \frac{3}{5} )}^{4} \times 1 }{( - \frac{3}{5} )}$

$\sf \longmapsto \large {( \frac{ - 3}{5}) }^{4 - 1} = \bold{ \red{{( \frac{ - 3}{5}) }^{3} }}(answer)$

Learn concepts:

✚When bases are same the powers gets added in multiplication and gets substracted during division.

✚If any constant or Variable having power of zero will be equal to 1.

✚If a fraction having degree of negative when we reciprocal it then it's power becomes+ve and vice -versa.

$\sf \longmapsto\large {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\sf \longmapsto \large\dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\sf \longmapsto\large {a}^{0} = 1$