Algebra Examples

$(\sqrt[7]{x^{2}}) (\sqrt[5]{x^{3}})$

Step 1

Rewrite the expression using the least common index of $35$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{x^{2}}$ as $x^{\frac{2}{7}}$ .

$x^{\frac{2}{7}} \sqrt[5]{x^{3}}$

Step 1.2

Rewrite $x^{\frac{2}{7}}$ as $x^{\frac{10}{35}}$ .

$x^{\frac{10}{35}} \sqrt[5]{x^{3}}$

Step 1.3

Rewrite $x^{\frac{10}{35}}$ as $\sqrt[35]{x^{10}}$ .

$\sqrt[35]{x^{10}} \sqrt[5]{x^{3}}$

Step 1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x^{3}}$ as $x^{\frac{3}{5}}$ .

$\sqrt[35]{x^{10}} x^{\frac{3}{5}}$

Step 1.5

Rewrite $x^{\frac{3}{5}}$ as $x^{\frac{21}{35}}$ .

$\sqrt[35]{x^{10}} x^{\frac{21}{35}}$

Step 1.6

Rewrite $x^{\frac{21}{35}}$ as $\sqrt[35]{x^{21}}$ .

$\sqrt[35]{x^{10}} \sqrt[35]{x^{21}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[35]{x^{10} x^{21}}$

Step 3

Multiply $x^{10}$ by $x^{21}$ by adding the exponents.

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Step 3.1

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

$\sqrt[35]{x^{10 + 21}}$

Step 3.2

Add $10$ and $21$ .

$\sqrt[35]{x^{31}}$