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mash [69]
3 years ago
8

What is the simplified form of the following expression? Assume y=0 ^3 sqrt 12x^2/16y

Mathematics
2 answers:
USPshnik [31]3 years ago
8 0

Answer: choice D

Step-by-step explanation: took it on edge

pochemuha3 years ago
7 0

For this case we must simplify the following expression:

\sqrt [3] {\frac {12x ^ 2} {16y}}

We rewrite the expression as:

\sqrt[3]{\frac{4(3x^2)}{4(4y)}}=\\\sqrt[3]{\frac{4(3x^2)}{4(4y)}}=\\\frac{\sqrt[3]{3x^2}}{\sqrt[3]{4y}}=

We multiply the numerator and denominator by:

(\sqrt[3]{4y})^2:\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{\sqrt[3]{4y}*(\sqrt[3]{4y})^2}=

We use the rule of powera ^ n * a ^ m = a ^ {n + m} in the denominator:

\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{(\sqrt[3]{4y})^3}=\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{4y}=

Move the exponent within the radical:

\frac{\sqrt[3]{3x^2}*(\sqrt[3]{16y^2}}{4y}=\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{2^3*(2y^2)}}{4y}=

\frac{2\sqrt[3]{3x^2}*(\sqrt[3]{(2y^2)}}{4y}=\\\frac{2\sqrt[3]{6x^2*y^2}}{4y}=

\frac{\sqrt[3]{6x^2*y^2}}{2y}

Answer:

\frac{\sqrt[3]{6x^2*y^2}}{2y}

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