Question

if x=((3)/(2))^(2)times((2)/(3))^(-4) find the value of x^(-2)

Answer 1

GIVEN=>

$x = ( \frac{3}{2} ) {}^{2} \times ( \frac{2}{3} ) {}^{ - 4}$

to find

value of

=

$= x {}^{ - 2}$

solution=>

$= > x = ( \frac{3}{2}) {}^{2} \times ( \frac{2}{3} ) {}^{ - 4} ... (1$

now equition first -2 power put

$= > x {}^{ - 2} =( ( \frac{3}{2}) {}^{2} ) {}^{ - 2} \times ((\frac{2}{3} ){}^{ - 4} ) {}^{ - 2} \\ \\ = > x {}^{ - 2} = ( \frac{3}{2} ) {}^{2 \times - 2} \times ( \frac{2}{3} ) {}^{ - 4 \times - 2} \\ \\ = > x {}^{ - 2} = ( \frac{2}{3} ) {}^{4} \times ( \frac{2}{3}) {}^{8} \\ \\ = > x {}^{ - 2} = ( \frac{2}{3} ) {}^{4 + 8} \\ \\ = > x {}^{ - 2} =( \frac{2}{3} ) {}^{12}$

formula uses

$\star\pink{=>(a/b)^-n=(b/a)^n}$

$\star\pink{=>(a^n×a^m)=a^(m+n)}$

-----------------

answer=

-----------------

$= > x {}^{ - 2} = ( \frac{2}{3}) {}^{12}$

----------------------------------

I hope it helps you☺