Basic Math Examples

$\sqrt[5]{6} \cdot \sqrt[6]{7}$

Step 1

Rewrite the expression using the least common index of $30$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{6}$ as $6^{\frac{1}{5}}$ .

$6^{\frac{1}{5}} \sqrt[6]{7}$

Step 1.2

Rewrite $6^{\frac{1}{5}}$ as $6^{\frac{6}{30}}$ .

$6^{\frac{6}{30}} \sqrt[6]{7}$

Step 1.3

Rewrite $6^{\frac{6}{30}}$ as $\sqrt[30]{6^{6}}$ .

$\sqrt[30]{6^{6}} \sqrt[6]{7}$

Step 1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{7}$ as $7^{\frac{1}{6}}$ .

$\sqrt[30]{6^{6}} \cdot 7^{\frac{1}{6}}$

Step 1.5

Rewrite $7^{\frac{1}{6}}$ as $7^{\frac{5}{30}}$ .

$\sqrt[30]{6^{6}} \cdot 7^{\frac{5}{30}}$

Step 1.6

Rewrite $7^{\frac{5}{30}}$ as $\sqrt[30]{7^{5}}$ .

$\sqrt[30]{6^{6}} \sqrt[30]{7^{5}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[30]{6^{6} \cdot 7^{5}}$

Step 3

Raise $6$ to the power of $6$ .

$\sqrt[30]{46656 \cdot 7^{5}}$

Step 4

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

$\sqrt[30]{46656 \cdot 16807}$

Step 5

Multiply $46656$ by $16807$ .

$\sqrt[30]{784147392}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt[30]{784147392}$

Decimal Form:

$1.97915552 \dots$