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Find the value of each of the following:...

Find the value of each of the following:
( i ) `8^(@)`
( ii ) `(-3)^(@)`
( iii ) `4^(@)+5^(@)`
( iv ) `6^(@) xx 7^(@)`

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The correct Answer is:
To solve the question, we will evaluate each part step by step. ### Step-by-Step Solution: **(i) Calculate \( 8^0 \)** According to the exponent rules, any non-zero number raised to the power of 0 is equal to 1. Thus, \[ 8^0 = 1 \] **(ii) Calculate \( (-3)^0 \)** Similarly, for negative numbers, the same rule applies. Thus, \[ (-3)^0 = 1 \] **(iii) Calculate \( 4^0 + 5^0 \)** Using the same rule: \[ 4^0 = 1 \] \[ 5^0 = 1 \] Now, add the two results: \[ 4^0 + 5^0 = 1 + 1 = 2 \] **(iv) Calculate \( 6^0 \times 7^0 \)** Again, applying the exponent rule: \[ 6^0 = 1 \] \[ 7^0 = 1 \] Now, multiply the two results: \[ 6^0 \times 7^0 = 1 \times 1 = 1 \] ### Final Answers: - (i) \( 8^0 = 1 \) - (ii) \( (-3)^0 = 1 \) - (iii) \( 4^0 + 5^0 = 2 \) - (iv) \( 6^0 \times 7^0 = 1 \)
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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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