Home/ Pramod Ahluwalia/Answers
  1. Asked: In:

    Find: (i) 64^(1/2) (ii) 32^(1/5) (iii) 125^(1/3)

    Best Answer
    Pramod Ahluwalia

    (i) 64^(1/2) = (8^2)^1/2 = 8 (ii) 32^1/2 = (2^5)^1/5 = 2^(5×1/5) = 2 (iii) 125^1/3 = (5^3)^1/3 = 5^(3×1/3) = 5

    (i) 64^(1/2) = (8^2)^1/2 = 8
    (ii) 32^1/2 = (2^5)^1/5 = 2^(5×1/5) = 2
    (iii) 125^1/3 = (5^3)^1/3 = 5^(3×1/3) = 5

    See less
    • 2
  2. Asked: In:

    Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. 4x² – 3x + 7

    Best Answer
    Pramod Ahluwalia

    4x² – 3x + 7 Polynomials in one variable as it contains only one variable x.

    4x² – 3x + 7 Polynomials in one variable as it contains only one variable x.

    See less
    • 1
  3. Asked: In:

    Simplify: (i) 2^(2/3). 2^(1/5) (ii) (1/3^3)^7 (iii) (11^1/2)/(11^1/4) (iv) 7^(1/2) . 8^(1/2)

    Best Answer
    Pramod Ahluwalia

    (i) 2^(2/3).2^(1/5) = 2^((2/3)+(1/5)) = 2^((10+3)/15) = 2^(13/15) (ii) (1/3^3)^7 = (3^-3)^7 = 3^-21 (iii) (11^1/2)/(11^1/4) = 11^1/2 × 11^-1/4 = 11^((1/2)-(1/4)) = 11^(2-1 / 4) = 11^1/4 (iv) 7^1/2 . 8^1/2 = (7 × 8)^1/2 = 56^1/2

    (i) 2^(2/3).2^(1/5) = 2^((2/3)+(1/5)) = 2^((10+3)/15) = 2^(13/15)
    (ii) (1/3^3)^7 = (3^-3)^7 = 3^-21
    (iii) (11^1/2)/(11^1/4) = 11^1/2 × 11^-1/4 = 11^((1/2)-(1/4)) = 11^(2-1 / 4) = 11^1/4
    (iv) 7^1/2 . 8^1/2 = (7 × 8)^1/2 = 56^1/2

    See less
    • 2
  4. Asked: In:

    Find : (i) 9^(3/2) (ii)32^(2/5) (iii) 16^(3/4) (iv) 125^(-1/3)

    Best Answer
    Pramod Ahluwalia

    (i) 9^(3/2) = (3^2)^(3/2) = 3^(2×3/2) = 3^2 = 9 (ii) 32^(2/5) = (2^5)^(2/5) = 2^(5×2/5) = 2^2 = 4 (iii) 16^(3/4) = (2^4)^(3/2) = 2^(4×3/4) = 2^3 = 8 (iv) 125^(-1/3) = (5^3^(-1/3) = 5^(3×-1/3) = 5^-1 = 1/5 = 5

    (i) 9^(3/2) = (3^2)^(3/2) = 3^(2×3/2) = 3^2 = 9
    (ii) 32^(2/5) = (2^5)^(2/5) = 2^(5×2/5) = 2^2 = 4
    (iii) 16^(3/4) = (2^4)^(3/2) = 2^(4×3/4) = 2^3 = 8
    (iv) 125^(-1/3) = (5^3^(-1/3) = 5^(3×-1/3) = 5^-1 = 1/5 = 5

    See less
    • 2
  6. Asked: In:

    On comparing the ratios, a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the pair of linear equations are consistent, or inconsistent. 2x – 3y = 8; 4x – 6y = 9

    Pramod Ahluwalia

    2x - 3y = 8 4x -6y = 9 Here, a₁/a₂ = 2/4 = 1/2, b₁/b₂ = -3/-6 = 1/2 and c₁/c₂ = 8/9 ⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂, so, pair of linear equations are inconsistent. See here for video explanation =>

    2x – 3y = 8
    4x -6y = 9
    Here, a₁/a₂ = 2/4 = 1/2, b₁/b₂ = -3/-6 = 1/2 and c₁/c₂ = 8/9
    ⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂, so, pair of linear equations are inconsistent.

    See here for video explanation =>

    See less
    • 3