Evaluate x12.y−1.z23x^{\dfrac{1}{2}}.y^{-1}.z^{\dfrac{2}{3}}x21.y−1.z32 when x = 9, y = 2 and z = 8.
40 Likes
Substituting value of x, y and z in x12.y−1.z23x^{\dfrac{1}{2}}.y^{-1}.z^{\dfrac{2}{3}}x21.y−1.z32 we get,
⇒x12.y−1.z23=(9)12.(2)−1.(8)23=(32)12×12×(23)23=3×12×22=122=6.\Rightarrow x^{\dfrac{1}{2}}.y^{-1}.z^{\dfrac{2}{3}} = (9)^{\dfrac{1}{2}}.(2)^{-1}.(8)^{\dfrac{2}{3}} \\[1em] = (3^2)^{\dfrac{1}{2}} \times \dfrac{1}{2} \times (2^3)^{\dfrac{2}{3}} \\[1em] = 3 \times \dfrac{1}{2} \times 2^2 \\[1em] = \dfrac{12}{2} = 6.⇒x21.y−1.z32=(9)21.(2)−1.(8)32=(32)21×21×(23)32=3×21×22=212=6.
Hence, x12.y−1.z23x^{\dfrac{1}{2}}.y^{-1}.z^{\dfrac{2}{3}}x21.y−1.z32 = 6.
Answered By
20 Likes
If a = 3 and b = -2, find the values of:
(i) aa + bb
(ii) ab + ba
If x = 103 × 0.0099, y = 10-2 × 110, find the value of xy\sqrt{\dfrac{x}{y}}yx.
If x4y2z3 = 49392, find the values of x, y and z, where x, y and z are different positive primes.
If a6b−43=ax.b2y\sqrt[3]{a^6b^{-4}} = a^x.b^{2y}3a6b−4=ax.b2y, find x and y, where a, b are different positive primes.
