Algebra Examples

$\frac{2}{3} \sqrt{81} - \sqrt[3]{- 27} - \frac{4}{3} \sqrt[3]{729}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $81$ as $9^{2}$ .

$\frac{2}{3} \cdot \sqrt{9^{2}} - \sqrt[3]{- 27} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2}{3} \cdot 9 - \sqrt[3]{- 27} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $9$ .

$\frac{2}{3} \cdot (3 (3)) - \sqrt[3]{- 27} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.3.2

Cancel the common factor.

$\frac{2}{3} \cdot (3 \cdot 3) - \sqrt[3]{- 27} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.3.3

Rewrite the expression.

$2 \cdot 3 - \sqrt[3]{- 27} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.4

Multiply $2$ by $3$ .

$6 - \sqrt[3]{- 27} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.5

Rewrite $- 27$ as ${(- 3)}^{3}$ .

$6 - \sqrt[3]{{(- 3)}^{3}} - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.6

Pull terms out from under the radical, assuming real numbers.

$6 - - 3 - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.7

Multiply $- 1$ by $- 3$ .

$6 + 3 - \frac{4}{3} \cdot \sqrt[3]{729}$

Step 1.8

Rewrite $729$ as $9^{3}$ .

$6 + 3 - \frac{4}{3} \cdot \sqrt[3]{9^{3}}$

Step 1.9

Pull terms out from under the radical, assuming real numbers.

$6 + 3 - \frac{4}{3} \cdot 9$

Step 1.10

Cancel the common factor of $3$ .

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Step 1.10.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$6 + 3 + \frac{- 4}{3} \cdot 9$

Step 1.10.2

Factor $3$ out of $9$ .

$6 + 3 + \frac{- 4}{3} \cdot (3 (3))$

Step 1.10.3

Cancel the common factor.

$6 + 3 + \frac{- 4}{3} \cdot (3 \cdot 3)$

Step 1.10.4

Rewrite the expression.

$6 + 3 - 4 \cdot 3$

Step 1.11

Multiply $- 4$ by $3$ .

$6 + 3 - 12$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $6$ and $3$ .

$9 - 12$

Step 2.2

Subtract $12$ from $9$ .

$- 3$