Respuesta :

gmany

Answer:

[tex]\large\boxed{\left(x^{27}y\right)^\frac{1}{3}=x^9y^\frac{1}{3}=x^9\sqrt[3]{y}}[/tex]

Step-by-step explanation:

[tex]\left(x^{27}y\right)^\frac{1}{3}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(x^{27}\right)^\frac{1}{3}y^\frac{1}{3}=x^{(27)\left(\frac{1}{3}\right)}y^\frac{1}{3}=x^9y^\frac{1}{3}\\\\\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=x^9\sqrt[3]{y}[/tex]

Answer:

The equivalent form of the given expression is  [tex]x^{9}\times\sqrt[3]{y}[/tex]                              

Step-by-step explanation:

Given : Expression [tex](x^{27}y)^\frac{1}{3}[/tex]

To find : The expression is equivalent to?

Solution :

Step 1 - Write the expression

[tex](x^{27}y)^\frac{1}{3}[/tex]

Step 2 - Separating the power using [tex](xy)^a=x^a\times y^a[/tex]

[tex]=(x^{27})^{\frac{1}{3}}\times y^{\frac{1}{3}}[/tex]

Step 3 - Solving the power, [tex](x^a)^b=x^{a\times b}[/tex]

[tex]=x^{27\times\frac{1}{3}}\times y^{\frac{1}{3}}[/tex]

Step 4 - Simplifying

[tex]=x^{9}\times\sqrt[3]{y}[/tex]           

So, The equivalent form of the given expression is [tex]x^{9}\times\sqrt[3]{y}[/tex]           

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