Question

If the expression x^{-\frac{3}{2}}y\sqrt{36xy^2}x − 2 3 ​ y 36xy 2 ​ is written in the form ax^by^cax b y c , then what is the product of a,a, bb and cc?

Answer 1

Answer:

-12

Step-by-step explanation:

The given expression is

$x^{-\frac{3}{2}}y\sqrt{36xy^2}$

We have to rewrite the given function in the form of  

$ax^{b}y^c$          ....(i)

then we have to find the product of a,b and c.

The given expression can be rewritten as

$x^{-\frac{3}{2}}y\sqrt{36}\sqrt{x}\sqrt{y^2}$

Using properties of exponents we get

$x^{-\frac{3}{2}}y6x^{\frac{1}{2}}y$       $[\because \sqrt[n]{a}=a^{\frac{1}{n}}]$

$6x^{-\frac{3}{2}+\frac{1}{2}}y^{1+1}$      $[\because a^ma^n=a^{m+n}]$

$6x^{-1}y^{2}$      ...(ii)

On comparing (i) and (ii), we get

$a=6,b=-1,c=2$

Product of a,b and c is

$abc=(6)(-1)(2)=-12$

Therefore, the product of a,b, and c is -12.