Rationalize and simplify the expression (x^(1/2))/(y^(1/2))

 Exercise

$\frac{\sqrt{x}}{\sqrt{y}}$

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To rationalize the denominator of the fraction, we multiply the numerator and denominator by $\sqrt{y}$

$\frac{\sqrt{x}}{\sqrt{y}}\frac{\sqrt{y}}{\sqrt{y}}$

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Multiplying fractions $\frac{\sqrt{x}}{\sqrt{y}} \times \frac{\sqrt{y}}{\sqrt{y}}$

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

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When multiplying two powers that have the same base ($\sqrt{y}$), you can add the exponents

$\frac{\sqrt{x}\sqrt{y}}{y}$

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Apply the property of power of a product in reverse: $a^n\cdot b^n=(a\cdot b)^n$

$\frac{\sqrt{xy}}{y}$

$\frac{\sqrt{xy}}{y}$

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