Basic Math Examples

$\sqrt[3]{7} \cdot \sqrt[5]{z}$

Step 1

Rewrite the expression using the least common index of $15$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7}$ as $7^{\frac{1}{3}}$ .

$7^{\frac{1}{3}} \sqrt[5]{z}$

Step 1.2

Rewrite $7^{\frac{1}{3}}$ as $7^{\frac{5}{15}}$ .

$7^{\frac{5}{15}} \sqrt[5]{z}$

Step 1.3

Rewrite $7^{\frac{5}{15}}$ as $\sqrt[15]{7^{5}}$ .

$\sqrt[15]{7^{5}} \sqrt[5]{z}$

Step 1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{z}$ as $z^{\frac{1}{5}}$ .

$\sqrt[15]{7^{5}} z^{\frac{1}{5}}$

Step 1.5

Rewrite $z^{\frac{1}{5}}$ as $z^{\frac{3}{15}}$ .

$\sqrt[15]{7^{5}} z^{\frac{3}{15}}$

Step 1.6

Rewrite $z^{\frac{3}{15}}$ as $\sqrt[15]{z^{3}}$ .

$\sqrt[15]{7^{5}} \sqrt[15]{z^{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[15]{7^{5} z^{3}}$

Step 3

Raise $7$ to the power of $5$ .

$\sqrt[15]{16807 z^{3}}$