Question

Chapter: Exponents and power
Board : CISCE

Answer 1

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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