Question

The simplified value of (give full explanation)​

Answer 1

Question

$\sf\large \dfrac{\bigg( { \dfrac{ - 3}{4}\bigg) }^{4} \times \dfrac{125}{27} }{ { \bigg(\dfrac{5}{3}\bigg) }^{2} \times \bigg(\dfrac{9}{16}\bigg )}$

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

$\sf\longmapsto\dfrac{\bigg( { \dfrac{ - 3}{4}\bigg) }^{4} \times \dfrac{ {5}^{3} }{ {3}^{3} } }{ { \bigg(\dfrac{5}{3}\bigg) }^{2} \times\bigg (\dfrac{ {3}^{2} }{ {4}^{2} }\bigg )}$

$\sf \longmapsto \dfrac{ { \bigg(\dfrac{ - 3}{4}\bigg )}^{4} \times {\bigg (\dfrac{5}{3}\bigg) }^{3} }{ {\bigg( \dfrac{5}{3}\bigg )}^{2} \times {\bigg( \dfrac{3}{4}\bigg )}^{2} }$

Concepts :

If bases are same then their power gets added in multiplication and gets substracted in division.

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

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

$\sf \large \longmapsto { \bigg(\dfrac{ - 3}{4}\bigg) }^{4 - 2} \times { \bigg(\dfrac{5}{3} \bigg)}^{3 - 2}$

$\sf \large\longmapsto { \bigg(\dfrac{ - 3}{4} \bigg)}^{2} \times \dfrac{5}{3}$

$\sf \longmapsto \large \dfrac{9}{16} \times \dfrac{5}{3} = \dfrac{3}{16} \times 5 = \dfrac{15}{16}$

Answer 2

Answer:

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Step-by-step explanation:

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