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solve for the product a b and c when you put [tex]\frac{\sqrt{4xy^3}}{x^\frac{3}{2}y\frac{7}{2} }[/tex] in the form [tex]ax^by^c[/tex] ?

solve for the product a b and c when you put texfracsqrt4xy3xfrac32yfrac72 tex in the form texaxbyctex class=

Respuesta :

LammettHash

It helps to write root expressions as rational powers. That is, [tex]\sqrt[n]{x} = x^{\frac1n}[/tex]

Then we have

[tex]\dfrac{\sqrt{4xy^3}}{x^{\frac32} y^{\frac72}} = \sqrt4 \cdot \dfrac{x^{\frac12} y^{\frac32}}{x^{\frac32} y^{\frac72}} = 2x^{\frac12-\frac32} y^{\frac32-\frac72} = 2x^{-1}y^{-2}[/tex]

so that a = 2, b = -1, and c = -2, and thus abc = 4.

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