Answer:
The equivalent expression is
[tex]4x^3y^2\sqrt[3]{4xy}[/tex]
Step-by-step explanation:
we have the expression
[tex]\sqrt[3]{256x^{10}y^{7}}[/tex]
Remember these properties
[tex]\sqrt[n]{x^m} =x^{\frac{m}{n}}[/tex]
[tex](x^{m})^{n} =x^{m*n}[/tex]
[tex](x^{m})(x^{n})=x^{m+n}[/tex]
so
[tex]\sqrt[3]{256x^{10}y^{7}}=(256x^{10}y^{7})^{\frac{1}{3}}=(256^{\frac{1}{3}})(x^{\frac{10}{3}})(y^{\frac{7}{3}})[/tex]
Rewrite the expression
[tex]256=(4^3)(2^2)[/tex]
[tex]x^{10}=(x^9)(x)[/tex]
[tex]y^7=(y^6)(y)[/tex]
substitute
[tex](256x^{10}y^{7})^{\frac{1}{3}}=((4^3)(2^2)(x^9)(x)(y^6)(y))^{\frac{1}{3}}[/tex]
Applying properties of exponents
[tex]((4^3)(2^2)(x^9)(x)(y^6)(y))^{\frac{1}{3}}=(4^3)^{\frac{1}{3}}(2^2)^{\frac{1}{3}}(x^9)^{\frac{1}{3}}(x)^{\frac{1}{3}}(y^6)^{\frac{1}{3}}(y)^{\frac{1}{3}}[/tex]
simplify
[tex](4)^{\frac{3}{3}}(2)^{\frac{2}{3}}(x)^{\frac{9}{3}}(x)^{\frac{1}{3}}(y)^{\frac{6}{3}}(y)^{\frac{1}{3}}[/tex]
[tex](4)(2)^{\frac{2}{3}}(x)^{3}(x)^{\frac{1}{3}}(y)^{2}(y)^{\frac{1}{3}}[/tex]
[tex]4x^3y^2\sqrt[3]{4xy}[/tex]
Answer:
the correct answer is B
Step-by-step explanation:
hope this helps
