Question

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

Answer 1

$x =( \frac{3}{2} )^{2} \times ( \frac{2}{3} )^{ - 4} \\x = \frac{ {3}^{6} }{ {2}^{6} } \\so \: \: \: \: \: {x}^{ - 2} = \frac{ {2}^{12} }{ {3}^{12} } \\ x = ( \frac{2}{3} )^{12}$
hope this helps

Answer 2

Hi,

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we know that ,

1 )( a / b )^-n = ( b/a )^n

2 ) a^m × a^n = a ^m+n

3 ) ( a^m )^n = a^mn

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x = ( 3/2 )^2 × ( 2/3 ) ^-4

x = ( 3/2 )² × ( 3/2 )⁴

x = ( 3/2 )^ 2 + 4

x = ( 3/2 )^6

x ^-2 = [ ( 3/2 )^6 ]^-2

= ( 3/2 ) ^ -12

= ( 2/3 )^12

I hope this helps you .

:)