Question

What is the following quotient?6-3(^3√6)/3/9

Answer 1

Applying properties of exponents, the quotient is given as follows:

$2\sqrt[3]{3} - \sqrt[3]{18}$

What is the quotient?

The expression is given by:

$\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}}$

The 3 can be inserted into the cube root, as follows:

$\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}} = \frac{6 - \sqrt[3]{6 \times 3³}}{\sqrt[3]{9}}$

Applying the subtraction, we have that the expression is:

$\frac{6}{\sqrt[3]{9}} - \frac{\sqrt[3]{162}}{\sqrt[3]{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{\frac{162}{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{18}$

The denominator can be simplified as follows:

$\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{\frac{2}{3}}$

Then:

$\frac{6}{\sqrt[3]{9}} = \frac{2 \times 3}{3^{\frac{2}{3}}} = 2 \times 3^{1 - \frac{2}{3}} = 2 \times 3^{\frac{1}{3}} = 2\sqrt[3]{3}$

Hence the quotient is given by:

$2\sqrt[3]{3} - \sqrt[3]{18}$

More can be learned about properties of exponents at brainly.com/question/25263760

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