Chapter: Exponents and power
Board : CISCE
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Solution:
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We know the Exponential laws:
i) x^m × x^n = x^m+n
ii) If x^m = x^n then m = n
iii) x^m/x^n = x^m-n
algebraic identity:
(a-b)(a²+ab+b²) = a³-b³
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Now ,
i) (2/9)³ + (2/9)^-6 = (2/9)^2x-1
=> (2/9)^3-6 = (2/9)^2x-1
=> (2/9)^-6 = (2/9)^2x-1
=> -6 = 2x-1
=> -6+1 = 2x
=> -5 = 2x
=> (-5/2) = x
Therefore,
x = -5/2
ii ) (x^a/x^b)^(a²+ab+b²) ×
(x^b/x^c)^(b²+bc+c²)
= (x^a-b)^(a²+ab+b²)×(x^b-c)^(b²+bc+c²)
= x^(a-b)(a²+ab+b²) ×
x^(b-c)(b²+bc+c²)
= x^(a³-b³) × x^(b³-c³)
= x^(a³-b³+b³-c³)
= x^a³-c³
••••
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