# How do you simplify sqrt(49x^5y^6)?

May 29, 2015

You just need to remember some exponenential rules:

• ${a}^{\frac{n}{m}} = \sqrt[m]{{a}^{n}}$

• $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}$

• ${a}^{n} \cdot {a}^{m} = {a}^{n + m}$

• ${\left({a}^{n}\right)}^{m} = {a}^{n \cdot m}$

Thus

$\sqrt{7 \cdot 7 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y}$

$\sqrt{{7}^{2} \cdot {\left({x}^{2}\right)}^{2} \cdot x \cdot {\left({y}^{3}\right)}^{2}}$

$7 {x}^{2} {y}^{3} \sqrt{x}$