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

Simplify:
( i ) `[{(frac(-1)(4))^(2)}^(-2)]^(-1)`
( ii ) `{(frac(-2)(3))^(2)}^(3)`
( iii ) `(frac(-3)(2))^(2) div (frac(-3)(2))^(6)`
( iv ) `(frac(-2)(3))^(7) div (frac(-2)(3))^(4)`

Text Solution

Verified by Experts

The correct Answer is:
(i) `frac(1)(256)`
(ii) `frac(64)(729)`
(iii) `frac(-8)(27)`
(iv) `frac(-8)(27)`
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(frac(-2)(3))^(10) div (frac(-2)(3))^(8)= ?

(frac(-2)(5))^(7) div (frac(-2)(5))^(5)= ?

(frac(-1)(5))^(3) div (frac(-1)(5))^(8)= ?

{(frac(1)(3))^(2)}^(4)= ?

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EXAMPLE 9. Simplify: [{frac(-1)(3)^(2)}^(-2)]^(-1)

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)

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

Simplify each of the following and express each as a rational number: ( i ) (frac(2)(3))^(4) xx (frac(2)(3))^(2) ( ii ) (frac(-3)(4))^(3) xx (frac(-3)(4))^(2) ( iii ) (frac(5)(7))^(5) xx (frac(5)(7))^(-3) ( iv ) (frac(-3)(5))^(-3) xx (frac(-3)(5))^(2)

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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