Write with Rational (Fractional) Exponents square root of 5* cube root of 5* fourth root of 5

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

Step 1

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

$5^{\frac{1}{2}} \cdot \sqrt[3]{5} \cdot \sqrt[4]{5}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}} \cdot \sqrt[4]{5}$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{5}$ as $5^{\frac{1}{4}}$ .

$5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}} \cdot 5^{\frac{1}{4}}$