Question

Please help me with this equation

Answer 1

Answer:
`(1)/(16)x^(-5)y^(-2)z^(4)`

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)=(1)/(16)x^(-5)y^(-2)z^(4)`