Question

I'm blanking on how to do this, I learned it so long ago, any help would be greatly appreciated. More interested on how to do it than the answer.

Answer 1

Answer:

$\dfrac{16 y^{22}}{x^{10}z^{10}}$

Step-by-step explanation:

Given expression is ,

$\sf\longrightarrow \bigg(\dfrac{2x^3y^{-5}z^8}{8x^{-2}y^6z^3}\bigg)^{-2}$

This would be simplified using the law of exponents , some of which I will use here are ,

• $(an)^m = a^m n^m$
• $\dfrac{a^m}{a^n}=a^{m-n}$

• $a^m a^n = a^{m+n}$
• $a^{-n} = \dfrac{1}{a^n}$

Using the above laws ,

$\sf \longrightarrow \bigg[ \dfrac{2}{8} \bigg(\dfrac{x^3}{x^{-2}}\bigg)\bigg(\dfrac{y^{-5}}{y^6}\bigg)\bigg(\dfrac{z^8}{z^3}\bigg) \bigg]^{-2}$

Using the second law mentioned above , we have,

$\sf \longrightarrow \bigg[ \dfrac{1}{4}(x^{3+2})(y^{-5-6})(z^{8-3})\bigg]^{-2}$

Simplify ,

$\sf \longrightarrow \bigg[\dfrac{1}{4} x^5y^{-11}z^5\bigg]^{-2}$

Using the first law mentioned above , we have,

$\sf \longrightarrow \bigg[ \dfrac{1}{4^{-2}} x^{5(-2)} y^{-11(-2)} z^{5(-2)}\bigg]$

Simplify,

$\sf \longrightarrow 4^2x^{-10}y^{22} z^{-10}$

Finally using the fourth law mentioned above , we have ,

$\sf \longrightarrow \boxed{\bf \dfrac{16 y^{22}}{x^{10}z^{10}}}$

Option K is the correct answer.