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svlad2 [7]
3 years ago
5

Using radicals what is an equivalent expression of y 1/5

Mathematics
1 answer:
valentina_108 [34]3 years ago
4 0
\bf a^{\frac{{ n}}{{ m}}} \implies  \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\
y^{\frac{1}{5}}\implies \sqrt[5]{y^1}\implies \sqrt[5]{y}
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======================================================

Explanation:

Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.

We have a right triangle with legs of 4 and 3. The hypotenuse is \sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5 through use of the pythagorean theorem.

We have a 3-4-5 right triangle.

Therefore, the vector is 5 units long. This is the magnitude of the vector.

Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.

Therefore, we go from < -4, 3 > to < -4/5,  3/5 >

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