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Express each of the following as a ratio...

Express each of the following as a rational number of the form `p/q :` (i)`5^(-3)` (ii) `(-2)^(-5)` (iii) `(4/3)^(-3)` (iv)`((-2)/5)^(-4)` (v) `1/(2^(-3))`

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To express each of the given expressions as a rational number of the form \( \frac{p}{q} \), we will use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \) or \( \frac{b}{a^{-n}} = \frac{a^n}{b} \). Let's solve each part step by step: ### (i) \( 5^{-3} \) 1. **Apply the negative exponent rule**: \[ ...
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RD SHARMA-POWERS-All Questions
  1. Express each of the following as a rational number of the form p/q :...

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  2. Express each of the rational number of the form p/q : (i)(3/8)^(-2)...

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  3. Express each of the rational number of the form p/q : (i)((-2)/7)^(...

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  4. Express each of the following as power of a rational number with pos...

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  5. Simplify : (2^(-1)-:5^(-1))^2xx\ ((-5)/8)^(-1)

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  6. Simplify : (5^(-1)xx\ 3^(-1))^(-1)-:6^(-1)

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  7. Simplify : (4^(-1)+\ 8^(-1))-:(2/3)^(-1)

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  8. Simplify : (1/4)^(-2)+\ (1/2)^(-2)+(1/3)^(-2)

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  9. Simplify : {6^(-1)+\ (3/2)^(-1)}^(-1)

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  10. Express each of the following as a rational number of the form p/q : ...

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  11. By what number should (-8)^-1 be multiplied so that the product may be...

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  12. By what number should (-24)^(-1) be divided so that the quotient may b...

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  13. Express each of the following as a rational number of the form p/q, wh...

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  14. Find the values of each of the following : (i)3^(-1)+4^(-1) (ii) (3...

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  15. Find the values of each of the following : (i)(1/2)^(-1)+\ (1/3)^(-1...

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  16. Find the values of each of the following : (i)(2^(-1)xx\ 4^(-1))-:2^...

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  17. Simplify : (i)(4^(-1)xx\ 3^(-1))^2 (ii) (5^(-1)-:6^(-1))^3 (iii)...

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  18. Simplify : (i)(3^2+2^2)xx\ (1/2)^3 (ii) (3^2-\ 2^2)xx\ (2/3)^(-3)

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  19. Simplify : (i)[(1/3)^(-3)-\ (1/2)^(-3)]-:(1/4)^(-3) (ii)(2^2+\ 3^2...

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  20. By what number should 5^(-1)be multiplied so that the product may be e...

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