What is the simplest radical form of the expression? (x ^ 4 * y ^ 7) ^ (2/3)
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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:
\(x^{\frac{8}{3}}y^{\frac{14}{3}}\)