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Simplify the following: (i)\ (5^(n+3)-\ ...

Simplify the following: `(i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2\ xx\ 5^n)` `(ii)\ (6(8)^(n+1)+\ 16(2)^(3n-2))/(10(2)^(3n+1)-7\ (8)^n)`

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Let's simplify the given expressions step by step. ### Part (i) Expression: \[ \frac{5^{(n+3)} - 6 \cdot 5^{(n+1)}}{9 \cdot 5^n - 2^2 \cdot 5^n} \] ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
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  2. Simplify the following: (i)\ (3^n\ xx\ 9^(n+1))/(3^(n-1)\ xx\ 9^(n-1))...

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  3. Simplify the following: (i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^...

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  4. Solve the following equations for x (i)7^(2x+3)=1 (ii)2^(x+1)=4^x (...

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  5. Solve the following equations for x\ : (i)\ 4^(2x)=1/(32)\ (ii)4^(x-1...

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  6. Solve the following equations for x\ : (i)\ 2^(2x)-\ 2^(x+3)+2^4=0 ...

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  7. If 49392=a^4b^2c^3, find the value of a ,\ b\ a n d\ c , where a ,\ b\...

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  8. If 1176=2^a xx\ 3^b xx\ 7^c , and a , b\ a n d\ c are natural numbers...

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  9. Given 4725=3^a5^b7^c , find the integral values of a ,\ b\ a n d\ c t...

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  10. If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r...

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  11. Find the value of: (8/(27))^(1/3)

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  12. Find the value of : ((32)/(243))^(1/5)

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  13. Find the value of: (1/(64))^(1/6)

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  14. Evaluate each of the following (i) (64)^(1/3) (ii)(125)^((-1)/3) (ii...

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  15. Evaluate each of the following by removing radical signs and negative ...

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  16. Simplify each of the following: (i)\ (625)^(-1/4) (ii)\ ((256)/(81))^(...

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  17. Simplify each of the following: (i)\ ((243)/(32))^(-4/5) (ii)\ (32...

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  18. [{(625)^(-1/4)}^(-1/2)]^2

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  19. Simplify: (256)^-(4^(((-3)/2)))

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  20. Simplify: 4/((216)^(-2/3))+1/((256)^(-3/4))+2/((243)^(-1/5))

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