Simplify (y^(1/6))^3* square root of x

${(y^{\frac{1}{6}})}^{3} \cdot \sqrt{x}$

Step 1

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

$y^{\frac{1}{6} \cdot 3} \cdot \sqrt{x}$

Step 2

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$y^{\frac{1}{3 (2)} \cdot 3} \cdot \sqrt{x}$

Cancel the common factor.

$y^{\frac{1}{3 \cdot 2} \cdot 3} \cdot \sqrt{x}$

Rewrite the expression.

$y^{\frac{1}{2}} \cdot \sqrt{x}$

$y^{\frac{1}{2}} \sqrt{x}$