Question

If x (3/2)^2 *(2/3)^-4

Answer 1

HEY!!

= (3/2)2*(3/2)4
Using the first law of exponents:-
am *an=a(m+n)
= (3/2)2*(3/2)4
= (3/2)2+4
= (3/2)6
Using the identity (a/b)m=(am/bm):-
= 36/26
= 729/64

Answer 2

Hi ,

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We know the exponential laws

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

2 ) a^m × a^n = a^m + n

3 ) ( a/b )^m = a^m / b^m

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Now ,

x = ( 3/2 )² ( 2/3 ) ^-4

= ( 3/2 )² ( 3/2 )⁴

= ( 3/2 )^ 2 + 4

= ( 3/2 )^6

= 3^6/ 2^6

= 729/64

I hope this helps you.

: )