Evaluate fourth root of 6^5* square root of 6^3

$\sqrt[4]{6^{5}} \cdot \sqrt{6^{3}}$

Step 1

Raise $6$ to the power of $5$ .

$\sqrt[4]{7776} \cdot \sqrt{6^{3}}$

Step 2

Rewrite $7776$ as $6^{4} \cdot 6$ .

Factor $1296$ out of $7776$ .

$\sqrt[4]{1296 (6)} \cdot \sqrt{6^{3}}$

Rewrite $1296$ as $6^{4}$ .

$\sqrt[4]{6^{4} \cdot 6} \cdot \sqrt{6^{3}}$

Step 3

Pull terms out from under the radical.

$6 \sqrt[4]{6} \cdot \sqrt{6^{3}}$

Step 4

Raise $6$ to the power of $3$ .

$6 \sqrt[4]{6} \cdot \sqrt{216}$

Step 5

Rewrite $216$ as $6^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$6 \sqrt[4]{6} \cdot \sqrt{36 (6)}$

Rewrite $36$ as $6^{2}$ .

$6 \sqrt[4]{6} \cdot \sqrt{6^{2} \cdot 6}$

Step 6

Pull terms out from under the radical.

$6 \sqrt[4]{6} \cdot (6 \sqrt{6})$

Step 7

Multiply $6 \sqrt[4]{6} (6 \sqrt{6})$ .

Multiply $6$ by $6$ .

$36 \sqrt[4]{6} \sqrt{6}$

Rewrite the expression using the least common index of $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$36 (6^{\frac{1}{2}} \sqrt[4]{6})$

Rewrite $6^{\frac{1}{2}}$ as $6^{\frac{2}{4}}$ .

$36 (6^{\frac{2}{4}} \sqrt[4]{6})$

Rewrite $6^{\frac{2}{4}}$ as $\sqrt[4]{6^{2}}$ .

$36 (\sqrt[4]{6^{2}} \sqrt[4]{6})$

Combine using the product rule for radicals.

$36 \sqrt[4]{6^{2} \cdot 6}$

Multiply $6^{2}$ by $6$ by adding the exponents.

Multiply $6^{2}$ by $6$ .

Raise $6$ to the power of $1$ .

$36 \sqrt[4]{6^{2} \cdot 6^{1}}$

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

$36 \sqrt[4]{6^{2 + 1}}$

Add $2$ and $1$ .

$36 \sqrt[4]{6^{3}}$

Step 8

Raise $6$ to the power of $3$ .

$36 \sqrt[4]{216}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$36 \sqrt[4]{216}$

Decimal Form:

$138.01171051 \dots$

Evaluate fourth root of 6^5* square root of 6^3

Related Questions

Support LCMGCF.com by disabling your adblocker.