How do I simplify $\frac{2 \sqrt{x} \cdot \sqrt{x^{3}}}{\sqrt{64 x^{15}}}$ $(2sqrt(x)*sqrt(x^3))/sqrt(64x^15)$ ?

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How do I simplify $\frac{2 \sqrt{x} \cdot \sqrt{x^{3}}}{\sqrt{64 x^{15}}}$ $(2sqrt(x)*sqrt(x^3))/sqrt(64x^15)$ ?

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Answer 1 · 2015-01-29T00:29:20

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

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

Note: $\sqrt{64 x^{15}}$ $sqrt(64x^15)$ = $8 x^{7} \sqrt{x}$ $8x^7sqrt(x)$

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

Now rationalize the denominator

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

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How do I simplify $\frac{2 \sqrt{x} \cdot \sqrt{x^{3}}}{\sqrt{64 x^{15}}}$ $(2sqrt(x)*sqrt(x^3))/sqrt(64x^15)$ ?

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