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Simplify each of the following as a rati...

Simplify each of the following as a rational number:
( i ) `(frac(4)(9))^(6) xx (frac(4)(9))^(-4)`
( ii ) `(frac(-7)(8))^(-3) xx (frac(-7)(8))^(2)`
( iii ) `(frac(4)(3))^(-3) xx (frac(4)(3))^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
(i) `frac(16)(81)`
(ii) `frac(-8)(7)`
(iii) `frac(243)(1024)`
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Simplify each of the following and express each as a rational number: ( i ) (frac(3)(2))^(4) xx (frac(1)(5))^(2) ( ii ) (frac(-2)(3))^(5) xx (frac(-3)(7))^(3) ( iii ) (frac(-1)(2))^(5) xx 2^(3) xx (frac(3)(4))^(2) ( iv ) (frac(2)(3))^(2) xx (frac(-3)(5))^(3) xx (frac(7)(2))^(2) ( v ) {(frac(-3)(4))^(3)-(frac(-5)(2))^(3)} xx 4^(2)

(frac(-3)(4))^(-3)= ?

Express each of the following as a rational number: ( i ) (frac(2)(3))^(3) ( ii ) (frac(-8)(5))^(3) ( iii ) (frac(-13)(11))^(2) ( iv ) (frac(1)(6))^(3) ( v ) (frac(-1)(2))^(5) ( vi ) (frac(-3)(4))^(4) ( vii ) (frac(-4)(7))^(3) ( viii ) (-1)^(9)

Express each of the following as a rational number: ( i ) 4^(-3) ( ii ) (-3)^(-5) ( iii ) (frac(1)(2))^(-4) ( iv ) (frac(-2)(5))^(-3)

Express each of the following as a rational number: ( i ) 5^(-3) ( ii ) (-2)^(-5) ( iii ) (frac(1)(4))^(-4) ( iv ) (frac(-3)(4))^(-3) ( v ) (-3)^(-1) xx (frac(1)(3))^(-1) ( vi ) (frac(5)(7))^(-1) xx (frac(7)(4))^(-1) ( vii ) (5^(-1)-7^(-1))^(-1) ( viii ) {(frac(4)(3))^(-1)-(frac(1)(4))^(-1)}^(-1) ( ix ) {(frac(3)(2))^(-1) div (frac(-2)(5))^(-1)} ( x ) (frac(23)(25))^(@)

Express each of the following as a rational number: ( i ) (4)^(-1) ( ii ) (-6)^(-1) (iii) (frac(1)(3))^(1) ( iv ) (frac(-2)(3))^(-1)

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Evaluate: ( i ) (frac(3)(4))^(2) ( ii ) (frac(-2)(3))^(3) ( iii ) (frac(-4)(5))^(5)

RS AGGARWAL-EXPONENTS -EXERCISE 5A
  1. Write each of the following in power notation: ( i ) frac(5)(7)xxfra...

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  2. Express each of the following in power notation: ( i ) frac(25)(36) ...

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  3. Express each of the following as a rational number: ( i ) (frac(2)(3...

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  4. Express each of the following as a rational number: ( i ) (4)^(-1) ...

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  5. Find the reciprocal of each of the following: ( i ) (frac(5)(8))^(4)...

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  6. Find the value of each of the following: ( i ) 8^(@) ( ii ) (-3)^(...

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  7. Simplify each of the following and express each as a rational number: ...

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  8. Simplify each of the following as a rational number: ( i ) (frac(4)(...

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  9. Express each of the following as a rational number: ( i ) 5^(-3) ( ...

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  10. Simplify: ( i ) [{(frac(-1)(4))^(2)}^(-2)]^(-1) ( ii ) {(frac(-2)...

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  11. By what number should (-5)^(-1) be multiplied so that the product is (...

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  12. By what number should 3^(-3) be multiplied to obtain 4?

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  13. By What number should (-30)^(-1) be divided to get 6^(-1) ?

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  14. Find x such that (frac(3)(5))^(3) xx (frac(3)(5))^(-6)=(frac(3)(5))^(2...

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  15. (3^5xx10^5xx25)/(5^7xx6^5)

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  16. Simplify: frac(16 xx 2^(n+1)-4 xx 2^(n))(16 xx 2^(n+2)-2 xx 2^(n+2)).

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  17. Find the value of n when: ( i ) 5^(2n) xx 5^(3)=5^(9) ( ii ) 8 xx...

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  18. If 2^(n-7) xx 5^(n-4)=1250, find the value of n.

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