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faltersainse [42]
2 years ago
10

What is the following quotient?

Mathematics
2 answers:
kvasek [131]2 years ago
8 0

Answer:

A

Step-by-step explanation:

mamaluj [8]2 years ago
4 0

Answer:

A.2(3^{\frac{1}{3}})-\sqrt[3]{18}

Step-by-step explanation:

We are given that

\frac{6-3(\sqrt[3]{6}}{\sqrt[3]{9}})

We have to find the quotient.

\frac{6}{\sqrt[3]{9}}-3(\frac{\sqrt[3]{6}}{\sqrt[3]{9}})

\frac{2\times 3}{\sqrt[3]{3^2}}-3(\frac{\sqrt[3]{3\times 2}}{\sqrt[3]{3^2}})

2\times\frac{3}{3^{\frac{2}{3}}}-3(\frac{2^{\frac{1}{3}}\times 3^{\frac{1}{3}}}{3^{\frac{2}{3}}})

Using the property

(ab)^n=a^n\cdot b^n

2\times 3^{1-\frac{2}{3}}-3(2^{\frac{1}{3}}\times 3^{\frac{1}{3}-\frac{2}{3}})

Using the property

\frac{a^x}{a^y}=a^{x-y}

2(3^{\frac{1}{3}})-3(2^{\frac{1}{3}}\times 3^{-\frac{1}{3}})

2(3^{\frac{1}{3}})-2^{\frac{1}{3}}\times 3^{1-\frac{1}{3}}

2(3^{\frac{1}{3}})-2^{\frac{1}{3}}\times 3^{\frac{2}{3}}

2(3^{\frac{1}{3}})-2^{\frac{1}{3}}\times \sqrt[3]{3^2}

2(3^{\frac{1}{3}})-2^{\frac{1}{3}}\times \sqrt[3]{9}

2(3^{\frac{1}{3}})-\sqrt[3]{2\times 9}

2(3^{\frac{1}{3}})-\sqrt[3]{18}

Hence, the quotient of \frac{6-3(\sqrt[3]{6}}{\sqrt[3]{9}}) is given by

2(3^{\frac{1}{3}})-\sqrt[3]{18}

Option A is correct.

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