Simplify the Radical Expression ( fourth root of 10)^4

${(\sqrt[4]{10})}^{4}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{10}$ as $10^{\frac{1}{4}}$ .

${(10^{\frac{1}{4}})}^{4}$

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10^{\frac{1}{4} \cdot 4}$

Step 3

Combine $\frac{1}{4}$ and $4$ .

$10^{\frac{4}{4}}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$10^{\frac{4}{4}}$

Rewrite the expression.

$10^{1}$

Step 5

Evaluate the exponent.

$10$