# How do I simplify (2sqrt(x)*sqrt(x^3))/sqrt(64x^15)?

Jan 29, 2015

$\frac{2 \sqrt{x} \cdot \sqrt{{x}^{3}}}{\sqrt{64 {x}^{15}}}$
1. Note: $\sqrt{x} \cdot \sqrt{{x}^{3}}$ = ${x}^{2}$

--> $\frac{2 \sqrt{x} \cdot \sqrt{{x}^{3}}}{\sqrt{64 {x}^{15}}}$ = $\frac{2 {x}^{2}}{\sqrt{64 {x}^{15}}}$

1. Note: $\sqrt{64 {x}^{15}}$ = $8 {x}^{7} \sqrt{x}$

--> $\frac{2 {x}^{2}}{\sqrt{64 {x}^{15}}}$ = $\frac{2 {x}^{2}}{8 {x}^{7} \sqrt{x}}$

1. Now rationalize the denominator

--> $\frac{2 {x}^{2}}{8 {x}^{7} \sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$ = $\frac{2 {x}^{2} \sqrt{x}}{8 {x}^{7} \cdot x}$ = $\frac{2 {x}^{2} \sqrt{x}}{8 {x}^{8}}$ = $\frac{\sqrt{x}}{4 {x}^{6}}$