Algebra Examples

$\sqrt[3]{d} \cdot \sqrt[3]{d} \cdot \sqrt[3]{d}$

Step 1

Multiply $\sqrt[3]{d}$ by $\sqrt[3]{d}$ .

${\sqrt[3]{d}}^{2} \cdot \sqrt[3]{d}$

Step 2

Multiply ${\sqrt[3]{d}}^{2}$ by $\sqrt[3]{d}$ by adding the exponents.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

Add $2$ and $1$ .

${\sqrt[3]{d}}^{3}$

Step 3

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

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Step 3.1

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

${(d^{\frac{1}{3}})}^{3}$

Step 3.2

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

$d^{\frac{1}{3} \cdot 3}$

Step 3.3

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

$d^{\frac{3}{3}}$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$d^{\frac{3}{3}}$

Step 3.4.2

Rewrite the expression.

$d^{1}$

Step 3.5

Simplify.

$d$