Algebra Examples

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

Step 1

Raise $5$ to the power of $3$ .

$\sqrt[4]{125} \cdot \sqrt{5}$

Step 2

Multiply $\sqrt[4]{125} \sqrt{5}$ .

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Step 2.1

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

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Step 2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\sqrt[4]{125} \cdot 5^{\frac{1}{2}}$

Step 2.1.2

Rewrite $5^{\frac{1}{2}}$ as $5^{\frac{2}{4}}$ .

$\sqrt[4]{125} \cdot 5^{\frac{2}{4}}$

Step 2.1.3

Rewrite $5^{\frac{2}{4}}$ as $\sqrt[4]{5^{2}}$ .

$\sqrt[4]{125} \sqrt[4]{5^{2}}$

Step 2.2

Combine using the product rule for radicals.

$\sqrt[4]{125 \cdot 5^{2}}$

Step 2.3

Rewrite $125$ as $5^{3}$ .

$\sqrt[4]{5^{3} \cdot 5^{2}}$

Step 2.4

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

$\sqrt[4]{5^{3 + 2}}$

Step 2.5

Add $3$ and $2$ .

$\sqrt[4]{5^{5}}$

Step 3

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

$\sqrt[4]{3125}$

Step 4

Rewrite $3125$ as $5^{4} \cdot 5$ .

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Step 4.1

Factor $625$ out of $3125$ .

$\sqrt[4]{625 (5)}$

Step 4.2

Rewrite $625$ as $5^{4}$ .

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

Step 5

Pull terms out from under the radical.

$5 \sqrt[4]{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[4]{5}$

Decimal Form:

$7.47674390 \dots$