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Ipatiy [6.2K]
3 years ago
15

Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y grea

ter-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
Mathematics
1 answer:
Nataly [62]3 years ago
6 0

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.

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