Question

Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y greater-than-or-equal-to 0 and z greater-than-or-equal-to 1 2 x squared z squared StartRoot 8 y cubed z EndRoot 4 x squared y z cubed StartRoot 2 x squared EndRoot 8 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot 64 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot

Answer 1

Answer:

Option C.

Step-by-step explanation:

The given expression is  

$\sqrt{128x^8y^3z^9}$

It can be written as

$\sqrt{(64\cdot 2)\cdot x^8\cdot y^{2+1}\cdot z^{8+1}}$

$=\sqrt{8^2\cdot 2\cdot (x^4)^2\cdot y^{2}\cdot y\cdot (z^{4})^2\cdot z}$

$=\sqrt{(8x^4yz^4)^2\cdot 2yz}$

$=8x^4yz^4\sqrt{2yz}$

Therefore, the correct option is C.