Question

Please help me with this equation

Answer 1

Answer: $\dfrac{1}{16}x^{-5}y^{-2}z^{4}$

Step-by-step explanation:

Given

Expression is $\left(4xy^3z^{-2}\right)^{-2}\cdot x^{-3}y^4z^0$

using the Exponent property that is

$[(a)^b]^c=a^{b\cdot c}\\a^x\cdot a^y=a^{x+y}$

Applying the above property

$\Rightarrow \left(4xy^3z^{-2}\right)^{-2}\cdot x^{-3}y^4z^0=4^{-2}x^{-2}y^{-6}z^{4}\cdot x^{-3}y^4z^0\\\\\Rightarrow \left(4xy^3z^{-2}\right)^{-2}\cdot x^{-3}y^4z^0=4^{-2}x^{-2-3}y^{-6+4}z^{4+0}\\\Rightarrow 4^{-2}x^{-5}y^{-2}z^{4}=\dfrac{1}{16}x^{-5}y^{-2}z^{4}$