Question

(-5/3)^6×(-5/3)^2m=(-5/3)^4
please solve this question ⁉️ fast ​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

$\implies( \frac{ - 5}{3} ) {}^{6} \times (\frac{ - 5}{3}) {}^{2m} = ( \frac{ - 5}{3} ) {}^{4}$

To find :

value of m

Solution :

$\implies( \frac{ - 5}{3} ) {}^{6} \times (\frac{ - 5}{3}) {}^{2m} = ( \frac{ - 5}{3} ) {}^{4}$

$\fbox{Identity used:}$

$⟶ {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\implies( \frac{ - 5}{3} ) {}^{6 + 2m} = ( \frac{ - 5}{3} ) {}^{4}$

When bases are same,powers can be compared

$\implies \: 6 + 2m = 4$

$\implies \: 2m = 4 - 6$

$\implies \: 2m = - 2$

$\implies \: m = \frac{ - 2}{ \: \: \: 2}$

$\implies \: m = - 1$

$\therefore \: m = - 1$

Answer 2

${\huge{\mathfrak{\orange{\fcolorbox{red}{green}{\underline{☑ansWer}}}}}}$

(-5/3)^6×(-5/3)^2m=(-5/3)^4

a^m×a^n=a^m+n

so,

(-5/3)^6+2m=(-5/3)^4

base are same so powers can be compared

6+2m=4

m=(4-6)/2

m= -2/2

m= -1