# How do you simplify (4x)^(1/2)*(9x)^(1/2)?

Jun 14, 2015

Use the rule ${x}^{\frac{m}{n}} = \sqrt[n]{{x}^{m}}$ ; n!=0
http://www.regentsprep.org/regents/math/algtrig/ato1/fractionalexp.htm
Solve as usual to get $6 x$.

#### Explanation:

${x}^{\frac{m}{n}} = \sqrt[n]{{x}^{m}}$ ; n=2="square root" ;m=1

${\left(4 x\right)}^{\frac{1}{2}} \cdot {\left(9 x\right)}^{\frac{1}{2}}$ =

$\sqrt{4 x} \cdot \sqrt{9 x}$ =

$2 \sqrt{x} \cdot 3 \sqrt{x}$ =

$2 \cdot 3 \sqrt{x} \sqrt{x}$ =

$6 \sqrt{{x}^{2}}$ =

$6 x$