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Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((...

Show that : `(x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1` `((x^(a+b))^2(x^(b+c))(x^(c+a))^2)/((x^a x^b x^c)^4)=1`

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

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

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

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

Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 (ii)\ {(x^(a-a^(-1)))^(1/(a-1))}^(a/(a+1))=x

Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a) (ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))

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

Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+\ x^(a-c))=1

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

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))

ICSE-INDICES [EXPONENTS]-EXERCISE 7 (B)
  1. Solve : 3^(x2) : 3^(x) = 9 : 1

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  2. Solve : 8 xx 2^(2x) + 4 xx 2^(x +1) = 1 + 2^(x)

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  3. Solve : 2^(2x) + 2^(x+2) - 4 xx 2^(3) = 0

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  4. Solve : (sqrt(3))^(x-3)=(sqrt(3))^((x+1)/4)

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  5. Find the values of m and n if : 4^(2m)=(root(3)(16))^(-(6)/(n))=(sqr...

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  6. Solve for x and y if : (sqrt(32))^(x)÷2^(y+1)= 1 and 8^(y)-16^(4-(x)...

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  7. If x is a positive real number and the exponents are rational numbe...

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  8. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

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  9. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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  10. If a^x=b^y=c^2a n d\ b^2=a c , prove that y=(2x z)/(x+z)

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  11. If 5^(-p)=4^(-q)=20^(r ). Show that (1)/(p)+(1)/(q)+(1)/(r )=0

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  12. If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y), show that ...

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  13. If 5^(x +1) = 25^(x-2), find the value of 3^(x-3) xx 2^(3-x).

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  14. If 4^(x+3)=112+8xx4^(x), find (18x)^(3x)

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  15. Solve for x : 4^(x-1)xx(0.5)^(3-2x)=((1)/(8))^(-x)

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  16. Solve for x : (a^(3x+5))^(2) . (a^(x))^(4) = a^(8x+12).

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  17. Solve for x : (81)^((3)/(4))-((1)/(32))^(-(2)/(5))+x((1)/(2))^(-1).2^(...

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  18. Solve for x : 2^((3x + 3)) = 2^((3x + 1)) + 48.

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  19. Solve for x : 3(2^(x) + 1) - 2^(x + 2)) + 5 = 0.

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  20. Solve for x : 9^(x + 2)) = 720 + 9^(x)

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