Simplify the Radical Expression -3/(2 cube root of 3)

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

Step 1

Multiply $\frac{3}{2 \sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

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

Step 2

Combine and simplify the denominator.

Multiply $\frac{3}{2 \sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \sqrt[3]{3} {\sqrt[3]{3}}^{2}}$

Move $\sqrt[3]{3}$ .

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

Raise $\sqrt[3]{3}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 {\sqrt[3]{3}}^{1 + 2}}$

Add $1$ and $2$ .

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 {\sqrt[3]{3}}^{3}}$

Rewrite ${\sqrt[3]{3}}^{3}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{3}$ as $3^{\frac{1}{3}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \cdot 3^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \cdot 3^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \cdot 3^{\frac{3}{3}}}$

Rewrite the expression.

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \cdot 3^{1}}$

Evaluate the exponent.

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \cdot 3}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{3 {\sqrt[3]{3}}^{2}}{2 \cdot 3}$

Rewrite the expression.

$- \frac{{\sqrt[3]{3}}^{2}}{2}$

Step 4

Simplify the numerator.

Rewrite ${\sqrt[3]{3}}^{2}$ as ${(3^{2})}^{\frac{1}{3}}$ .

$- \frac{\sqrt[3]{3^{2}}}{2}$

Raise $3$ to the power of $2$ .

$- \frac{\sqrt[3]{9}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt[3]{9}}{2}$

Decimal Form:

$- 1.04004191 \dots$

Simplify the Radical Expression -3/(2 cube root of 3)

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