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Step-by-step explanation:
16. (2/3)^ x-1 = (2/3)^2-x
Bases are same, equate the powers.
x-1 = 2-x
x= 2+1 -x
x+x= 3
2x=3
x=3/2
⇒x-1= 3/2 - 1
= 3/2 - 1x2/1x2
= 3/2-2/2
= 3-2/2
= 1/2
⇒ 2 -x= 2-3/2
= 2x2/1x2 - 3/2
= 4/2 - 3/2
= 4-3/2
= 1/2
(2/3)^1/2 = (2/3)^1/2.
17. (3^-1 - 5^-1)^-1 ÷ ( 2^-1 - 3^-1) ^ -1'
a^-m= 1/a^-m
= [ (1/3)^1 - (1/5)^1]^-1 ÷ [ (1/2)^1 - (1/3)^1] ^-1
= [ 1/3 - 1/5 ] ^-1 ÷ [ 1/2-1/3]^-1 {subtract them by finding LCM}
= [ 1x5/3x5 - 1x3/5x3]^-1 ÷ [1x3/2x3 - 1x2/3x2]^-1
= [ 5/15 - 3/15 ]^-1 ÷ [3/6 -2/6]^-1
= [2/15]^-1 ÷ [1/6]^-1
= (15/2)^1 ÷ (6/1)^1
=15/2 x 1/6
=15/12
=5/4
Hope it helps you. Take care.
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