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Murrr4er [49]
2 years ago
8

What is the simplified form of 12x/900x²y4z6?

Mathematics
1 answer:
zalisa [80]2 years ago
7 0

Answer:

360xy^2|xz^3|

Step-by-step explanation:

Given expression:

12x \sqrt{900x^2y^4z^6}

\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:

\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}

Replace 900 with 30² :

\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}

\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:

\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}

\implies 360x|x|\sqrt{y^4}\sqrt{z^6}

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:

\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}

Simplify:

\implies 360xy^2|xz^3|

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

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