Basic Math Examples

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

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

Step 1

Rewrite the expression using the least common index of

30

$30$ .

Tap for more steps...

Step 1.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt[5]{6}

$\sqrt[5]{6}$ as

6^{\frac{1}{5}}

$6^{\frac{1}{5}}$ .

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

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

Step 1.2

Rewrite

6^{\frac{1}{5}}

$6^{\frac{1}{5}}$ as

6^{\frac{6}{30}}

$6^{\frac{6}{30}}$ .

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

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

Step 1.3

Rewrite

6^{\frac{6}{30}}

$6^{\frac{6}{30}}$ as

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

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

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

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

Step 1.4

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt[6]{7}

$\sqrt[6]{7}$ as

7^{\frac{1}{6}}

$7^{\frac{1}{6}}$ .

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

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

Step 1.5

Rewrite

7^{\frac{1}{6}}

$7^{\frac{1}{6}}$ as

7^{\frac{5}{30}}

$7^{\frac{5}{30}}$ .

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

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

Step 1.6

Rewrite

7^{\frac{5}{30}}

$7^{\frac{5}{30}}$ as

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

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

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

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

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

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

Step 3

Raise

6

$6$ to the power of

6

$6$ .

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

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

Step 4

Raise

7

$7$ to the power of

5

$5$ .

\sqrt[30]{46656 \cdot 16807}

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

Step 5

Multiply

46656

$46656$ by

16807

$16807$ .

\sqrt[30]{784147392}

$\sqrt[30]{784147392}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\sqrt[30]{784147392}

$\sqrt[30]{784147392}$

Decimal Form:

1.97915552 \dots

$1.97915552 \dots$

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

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

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$