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Prove that: ((x^a)/(x^b))^a^2+a b+b^2x\ ...

Prove that: `((x^a)/(x^b))^a^2+a b+b^2x\ ((x6b)/(x^c))^b^2+b c+c^2\ x\ ((x^c)/(x^a))^c^2+c a+a^2`

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Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^a))^(c^(2+c a+a^2))

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a^2+a b+b^2)((x^b)/(x^c))^(b^2+b c+c^2)((x^c)/(x^a))^(c^2+c a+a^2)=1

Prove that: ((x^a)/(x^(b)))^(a^(2+a b+b^2))\ xx\ ((x^b)/(x^(c)))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^(a)))^(c^(2+c a+a^2))=1

If x is a positive real number and the exponents are rational numbers, Find: ((x^a)/(x^b))^(a^2+b^2-a b). ((x^b)/x^c)^(b^2+c^2-b c). ((x^c)/(x^(a)))^(c^2+a^2-c a)

Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

Simplify : ((x^(a))/(x^(-b)))^(a^(2)-ab+b^(2))xx((x^(b))/(x^(-c)))^(b^(2)-bc+c^(2))xx((x^(c))/(x^(-a)))^(c^(2)-ca+a^(2))

Show that : (i) x^(a(b-c))/(x^(b(a-c)))/((x^b)/(x^a))^c=1 , (ii) ((x^(a+b))^2(x^(b+c))^2(x^(c+a))^2)/((x^a x^b x^c)^4)=1

If f(x)=((x^2)/(x^b))^(a+b)*((x^b)/(x^c))^(b+c)*((x^c)/(x^a))^(c+a) , then f^(prime)(x) is equal to: (a) 1 (b) 0 (c) x^(a+b+c) (d) None of these

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(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)

ICSE-INDICES [EXPONENTS]-EXERCISE 7 (A)
  1. Evaluate : 7^(0)xx(25)^(-(3)/(2))-5^(-3)

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  2. Evaluate : ((16)/(81))^(-3//4)xx((49/9)^(3//2)/((343)/(216))^(2//3))

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  3. Simplify : ((8 x^(3)) /(125y^(3)))^((2)/(3))

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  4. Simplify : (a + b)^(-1) (a^(-1) + b^(-1))

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  5. Simplify : (5^(n+3)-6xx5^(n+1))/(9xx5^(n)-5^(n)xx2^(2))

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  6. Simplify : (3x^(2))^(-3)xx(x^(9))^((2)/(3))

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  7. Simplify: sqrt(1/4)+(0. 01)^(-1/2)-(27)^(2/3)

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  8. Evaluate : ((27)/(8))^((2)/(3))-((1)/(4))^(-2)+5^(0)

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  9. Simplify each of the folloiwing and express with positive index : (...

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  10. Simplify each of the folloiwing and express with positive index : (...

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  11. Simplify each of the folloiwing and express with positive index : (...

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  12. Simplify each of the folloiwing and express with positive index : [...

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  13. If 2160 = 2^(a). 3^(b) . 5^(c ), find a, b and c. Hence calculate the ...

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  14. If 1960=2^(a)xx5^(b)xx7^(c ), calculate the value of 2^(-a)xx7^(b)xx5^...

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  15. Simplify : (8^(3a)xx2^(5)xx2^(2a))/(8xx3^(3n)-5xx27^(n))

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  16. Simplify : (3xx27^(n+1)+9xx3^(3n-1))/(8xx3^(3n)-5xx27^(n))

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  17. Show that : ((a^(m))/(a^(-n)))^(m-n)xx((a^(n))/(a^(-1)))^(n-1)xx((a^...

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  18. If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^...

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  19. Prove that: ((x^a)/(x^b))^a^2+a b+b^2x\ ((x6b)/(x^c))^b^2+b c+c^2\ x\ ...

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  20. Simplify : ((x^(a))/(x^(-b)))^(a^(2)-ab+b^(2))xx((x^(b))/(x^(-c)))^...

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