Simplify (qr^6)^(1/2)

${(q r^{6})}^{\frac{1}{2}}$

Apply the product rule to $q r^{6}$ .

$q^{\frac{1}{2}} {(r^{6})}^{\frac{1}{2}}$

Multiply the exponents in ${(r^{6})}^{\frac{1}{2}}$ .

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

$q^{\frac{1}{2}} r^{6 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$q^{\frac{1}{2}} r^{2 (3) \frac{1}{2}}$

Cancel the common factor.

$q^{\frac{1}{2}} r^{2 \cdot 3 \frac{1}{2}}$

Rewrite the expression.

$q^{\frac{1}{2}} r^{3}$

Reorder factors in $q^{\frac{1}{2}} r^{3}$ .

$r^{3} q^{\frac{1}{2}}$