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State the quotient law of exponents...

State the quotient law of exponents

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The exponent rule for dividing exponential terms together is called the Quotient Rule.
Quotient rule simply states that as long as the base is the same, we can just divide two powers by subtracting the exponents.
For any real number `a` and natural numbers `m \and\n`, such that `m>n` .
`a^m/a^n=a^(m-n)`
The quotient law of exponents states that the exponent of the quotient is the difference between the exponents of the divisor and dividend.
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
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  2. When simplified (256)^-(4^((-3//2)\ )) is 8 (b) 1/8 (c) 2 (d) 1...

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  3. (5^(n+2) −6 xx 5^(n+1))/(3 xx 5^n − 2xx 5^(n+1)) is equal to ...

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  4. If a ,\ b ,\ c are positive real numbers, then sqrt(a^(-1)b)\ xx\ sqrt...

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  5. If (3^(2x-8))/(225)=(5^3)/(5^x) , then x= 2 (b) 3 (c) 5 (d) 4

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  6. If (2/3)^x\ \ (3/2)^(2x)=(81)/(16), . then x= 2 (b) 3 (c) 4 (d)...

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  7. If a ,\ b ,\ c are positive real numbers, then root(5)(3125\ a^(10)b^5...

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  8. The value of 64^(-1/3)\ (64^(1/3)-64^(2/3)), is 1 (b) 1/3 (c) -...

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  9. If sqrt(5^n)=125 , then 5^(nsqrt64 )= 25 (b) 1/(125) (c) 625 (d)...

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  10. If (16)^(2x+3)=(64)^(x+3), then 4^(2x-2)=64(b) 256 (c) 32 (d) 512

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  11. If a ,\ m ,\ n are positive integers, then {root(m)(sqrt a)}^(m n) is ...

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  12. If 2^(-m)\ xx1/(2^m)=1/4, then 1/(14)\ {(4^m)^(1//2)+\ (1/(5^m))^(-1)}...

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  13. If x=2\ \ and y=4, then (x/y)^(x-y)+\ (y/x)^(y-x)=

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  14. The value of m for which [{(1/(7^2))^(-2)}^(-1/3)]^(1/4)=7^m ,

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  15. If (2^(m+n))/(2^(m-n))=16 and a=2^(1/10) then ((a^(2m+n-p))^2)/((a^(m-...

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  16. The value of {(23+2^2)^(2/3)+\ (140-19)^(1/2)}^2 , is 196 (b) 289 (c...

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  17. If\ \ sqrt(2^n)=1024 ,\ \ then 3^(2(n/4-4))= 3 (b) 9 (c) 27 (d) ...

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  18. If (3^(5x)\ xx\ 81^2\ xx\ \ 6561)/(3^(2x))=3^7, then x= (a)\ 3 (b) ...

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  19. State the quotient law of exponents

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  20. The value of "{"8^(-4/3)-:2^(-2)")"^(1/2) is (a)1/2 (b) 2 (c) 1/4 (d...

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