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What is the simplest radical form of the expression? (x ^ 4 * y ^ 7) ^ (2/3)

 

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 Dec 16, 2019
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\(\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n\)

\(\left(x^4y^7\right)^{\frac{2}{3}}=\left(x^4\right)^{\frac{2}{3}}\left(y^7\right)^{\frac{2}{3}}\)

\(=\left(x^4\right)^{\frac{2}{3}}\left(y^7\right)^{\frac{2}{3}}\)

Simplify:

=\(x^{\frac{8}{3}}\left(y^7\right)^{\frac{2}{3}}\)

Simplify:

\(x^{\frac{8}{3}}y^{\frac{14}{3}}\)

 

Final answer:

\(x^{\frac{8}{3}}y^{\frac{14}{3}}\)

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 Dec 16, 2019

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