Algebra Examples

$d = {(\sqrt[3]{- 55})}^{3}$

Step 1

Remove parentheses.

$d = {\sqrt[3]{- 55}}^{3}$

Step 2

Simplify ${\sqrt[3]{- 55}}^{3}$ .

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Step 2.1

Rewrite $- 55$ as ${(- 1)}^{3} \cdot 55$ .

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Step 2.1.1

Rewrite $- 55$ as $- 1 (55)$ .

$d = {\sqrt[3]{- 1 (55)}}^{3}$

Step 2.1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$d = {\sqrt[3]{{(- 1)}^{3} \cdot 55}}^{3}$

Step 2.2

Pull terms out from under the radical.

$d = {(- 1 \sqrt[3]{55})}^{3}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Rewrite $- 1 \sqrt[3]{55}$ as $- \sqrt[3]{55}$ .

$d = {(- \sqrt[3]{55})}^{3}$

Step 2.3.2

Apply the product rule to $- \sqrt[3]{55}$ .

$d = {(- 1)}^{3} {\sqrt[3]{55}}^{3}$

Step 2.3.3

Raise $- 1$ to the power of $3$ .

$d = - {\sqrt[3]{55}}^{3}$

Step 2.4

Rewrite ${\sqrt[3]{55}}^{3}$ as $55$ .

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Step 2.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{55}$ as $55^{\frac{1}{3}}$ .

$d = - {(55^{\frac{1}{3}})}^{3}$

Step 2.4.2

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

$d = - 55^{\frac{1}{3} \cdot 3}$

Step 2.4.3

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

$d = - 55^{\frac{3}{3}}$

Step 2.4.4

Cancel the common factor of $3$ .

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Step 2.4.4.1

Cancel the common factor.

$d = - 55^{\frac{3}{3}}$

Step 2.4.4.2

Rewrite the expression.

$d = - 55^{1}$

Step 2.4.5

Evaluate the exponent.

$d = - 1 \cdot 55$

Step 2.5

Multiply $- 1$ by $55$ .

$d = - 55$