Answer:
[tex]\large \text{$ 4 x^{\frac{14}{3}}y^{\frac{8}{3}}$}[/tex]
Step-by-step explanation:
Given expression:
[tex](8x^7y^4)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a \cdot b)^c=a^{c} \cdot b^{c}:[/tex]
[tex]\implies 8^{\frac{2}{3}} \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]
[tex]\implies 4 \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 4 \cdot x^{\frac{14}{3}}\cdot y^{\frac{8}{3}}[/tex]
[tex]\implies 4 x^{\frac{14}{3}}y^{\frac{8}{3}}[/tex]
Expand [tex]\bf{(8x^{7}y^{4})^{\frac{2}{3} } }[/tex]
[tex]\bf{8^{\frac{2}{3} }(x^{7})^{\frac{2}{3} }(y^{4})^{\frac{2}{3} } }[/tex]
To raise a power to another power, multiply the exponents. Multiply 7 and 2/3 to get 14/3.
[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }(y^{4})^{\frac{2}{3} } }[/tex]
To raise a power to another power, multiply the exponents. Multiply 4 and 2/3 to get 8/3.
[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }y^{\frac{8}{3} } }[/tex]
Calculate 8 to the power of 2/3 and you get 2/4.
[tex]\bf{4x^{\frac{13}{4} }y^{\frac{8}{3} } \ \ ==== > \ \ \ Answer }[/tex]
