Question

evaluate (3/5) to the power -3​

Answer 1

Given :

$\sf \bigg( \dfrac{3}{5} \bigg)^{-3}$

To find :

It's value

Identity used :

$\sf \bullet \: \bigg( \dfrac{a}{b} \bigg)^{ - m} \: = \: \bigg(\dfrac{b}{a} \bigg)^{m} \\ \\ \sf \bullet \: \bigg( \dfrac{a}{b} \bigg)^{m} \: = \: \dfrac{ {a}^{m} }{ {b}^{m} }$

Solution :

$\sf \bigg( \dfrac{3}{5} \bigg)^{-3} \\ \\ \sf \implies \: \bigg( \dfrac{5}{3} \bigg)^{3} \\ \\ \sf \implies \: \dfrac{ {5}^{3} }{ {3}^{3} } \\ \\ \sf \implies \: \: \bold{\dfrac{125}{27} }$

ANSWER :

$\sf \bold{ \dfrac{125}{27} }$

Additional identity :

$\sf \bullet \: {a}^{m} \times {a}^{n} \: = {a}^{(m + n)} \\ \\ \sf \bullet \: \dfrac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{(m -n)} \\ \\ \sf \bullet \: { ({a}^{m} )}^{n} \: = \: {a}^{(m \times n)}$

Answer 2

Answer:

125/27 is the answer

Step-by-step explanation:

(3/5)^-3

(5/3)^3

5x5x5/3x3x3

125/27