Question

find the value of p for which (3/5)^p(5/3)^2p=125/27

Answer 1

$hy friend$

⇒(3/5)^x × (5/3)^2x.

= 125/27

So

⇒(5/3)^{-x} × (5/3)^2x

=125/27

Further simplifying the expression

(5/3)^x =125/27

(5/3)^x =(5/3)^3

So from here clearly x = 3

$thankyou brainly user$

Answer 2

Hi !

Identities used :

${( \frac{a}{b} )}^{m} = {( \frac{b}{a} )}^{ - m} \\ \\ {a}^{m} \times {a}^{n} = {a}^{m + n}$


${( \frac{3}{5} )}^{p} \times {( \frac{5}{3} )}^{2p} = \frac{125}{27}$

We can also write it as,

${( \frac{5}{3} )}^{ - p} \times {( \frac{5}{3} )}^{ 2p} = {( \frac{5}{3} )}^{3}$

As, the numbers are same, we can put the powers equal :

$- p + 2p = 3 \\ \\ p = 3$