Write with Rational (Fractional) Exponents eighth root of 75^4

$\sqrt[8]{75^{4}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{75^{4}}$ as $75^{\frac{4}{8}}$ .

$75^{\frac{4}{8}}$

Step 2

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$75^{\frac{4 (1)}{8}}$

Cancel the common factors.

Factor $4$ out of $8$ .

$75^{\frac{4 \cdot 1}{4 \cdot 2}}$

Cancel the common factor.

$75^{\frac{4 \cdot 1}{4 \cdot 2}}$

Rewrite the expression.

$75^{\frac{1}{2}}$