# Find the product of $(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z)$ and verify the result for ; $x=2, y=3$ and $z=-1$

Given :

The given expression is $(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z)$.

To do :

We have to find the product of the given expression and verify the result for $x=2, y=3$ and $z=-1$.

Solution :

$(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z)$

$(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z) = (-3 \times \frac{4}{9}\times \frac{-27}{2}) \times (x \times x^2 \times x) \times (y \times y^2) \times (z \times z \times z)$

$= (-3 \times 2 \times -3) \times x^{1+2+1} \times y^{1+2} \times z^{1+1+1}$

$= 18x^4 y^3 z^3$

If $x = 2, y = 3$ and $z = -1$ then $(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z) =$

$= 18x^4 y^3 z^3 = 18 (2)^4 (3)^3 (-1)^3$

$= 18(16)(9)(-1)$

$= -2592$.

Therefore, the value of  $(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z)$ at $x = 2, y = 3$ and $z = -1$ is $-2592$

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Updated on: 10-Oct-2022

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