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Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-...

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`

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Let's solve the two parts of the question step by step. ### Part (i): Show that \[ (x^{(a-b)})^{(a+b)} \cdot (x^{(b-c)})^{(b+c)} \cdot (x^{(c-a)})^{(c+a)} = 1 \] **Step 1:** Apply the power of a power property. ...
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Show that (x^(a+b))^(a-b)times(x^(b+c))^(b-c)times(x^(c+a))^(c-a)=1

Prove that (x^(b-c))^(a)(x^(a-b))^(c)(x^(c-a))^(b)=1

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

Simplify (x^(a-b))^(a+b).(x^(b-c))^(b+c).(x^((c-a)))^((c+a)) where x ne 0 and x ne 1 .

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

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

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

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

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

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. 1/(1+x^(a-b))+1/(1+x^(b-a))=?

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

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  3. Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 ...

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  4. Show that:(a^(x-y))^(x+y).(a^(y-z))^(y+z).(x^(z-x))^(z+x)=1

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  5. Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+...

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  6. If 2^x = 3^y =12^z show that 1/z= 1/y+2/x ​ ​

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  7. If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

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  8. If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

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  9. If 3^x=5^y=(75)^z show that z=(xy)/(2x+y

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  10. If 27^x=9/(3^x), find xdot

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  11. Find the values of x in each of the following : (i)2^(5x)-:2^x=25^(2...

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  12. Find the value of x in each of the following: (i)\ (3/5)^x\ (5/3)^(2x)...

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  13. Find the value of x in each of the following: (i)2^(x-7) xx 5^(x-4)=1...

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  14. Find the value of x in each of the following: (i)\ 5^(2x+3)=1 (ii)\ ...

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  15. If x=2^(1/3)+ 2^(2/3) show that x^3-6x=6

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  16. Determine (8x)^x , if 9^(x+2)=240+9^x

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  17. If 3^(x+1)=9^(x-2), find the value of 2^(1+x)

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  18. If 3^(4x)=(81)^(-1) and 10^(1/y)=0. 0001 , find the value of 2^(-x+4y)

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  19. If 5^(3x)=\ 125\ and 10^y=0. 001 find x\ a n d\ y C

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  20. .Solve the following equations: (i)\ 3^(x+1)=27\ xx\ 3^4 \ (ii)4^(...

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