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Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(...

Simplify that: `((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)`

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Express the following mathematical operations in scientific notation (1) (7.7 xx 10^(4))+ (0.77 xx 10^(5)) (2) (8.7 xx 10^(4))/(0.77 xx 10^(5))

Simplify : ( 16 xx 10 ^(4) xx 3^(3))/( 6^(5) xx 5^(6))

Express the following mathematical operations in scientific notation (1) (7.7 xx 10^(9))/(6.6 xx 10^(5)) (2) (7.7 xx 10^(-7))/(6.6 xx 10^(5))

Calculate the following a. (6.7 xx 10^(5)) xx (4.6 xx 10^(4)) b. (7.6 xx 10^(7)) xx (3.8 xx 10^(-4)) c. (6.8 xx 10^(-3)) xx (5.2 xx 10^(-4)) d. (6.7 xx 10^(5)) / (4.6 xx 10^(4)) e. (7.6 xx 10^(7)) / (3.8 xx 10^(-4)) f. (6.8 xx 10^(-3)) / (3.8 xx 10^(-4)) g. 7.65 xx 10^(2) + 2.72 xx 10^(3) h. 7.87 xx 10^(-4) - 2.61 xx 10^(-5)

Simplify. (i) (25 xx t^(-4))/(5^3 xx 10 xx t^(-8)) (t != 0) (ii) (3^(-5) xx 10^(-5) xx 125)/(5^(-7) xx 6^(-5))

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Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5))\ -:(3^(4/3)\ xx\ 5^(-7/5))/(4^(-3/5)\ xx\ 6)=10

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)

Express the following mathematical operations in scientific notation. (1) (7.7xx10^(4))+(0.77xx10^(5)) (2) (8.7xx10^(4))-(0.77xx10^(5))

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Simplify the following: 3(a^4b^3)^10xx5(a^2b^2)^3

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  2. Simplify that: (2x^(-2)y^3)^3

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  3. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

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  4. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

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  5. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

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  6. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

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  7. If a=3\ \ a n d\ b=-2\ , find the values of: (i)\ a^a+b^b (ii)\ a^b+b...

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

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

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

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  11. Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=1

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  12. Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-...

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  13. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

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  14. Prove that: (a^(-1)+b^(-1))^(-1)=(a b)/(a+b)

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  15. If a b c=1,\ show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

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

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

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

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

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

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