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[tex] \dfrac{(27y^{-2})^\frac{1}{3}}{y^{-\frac{2}{3}}}=(27)^\frac{1}{3}(y^{-2})^\frac{1}{3}:\dfrac{1}{y^\frac{2}{3}}=\sqrt[3]{27}y^{-2\cdot\frac{1}{3}}\cdot y^\frac{2}{3}\\\\=3y^{-\frac{2}{3}}\cdot y^\frac{2}{3}=3y^{-\frac{2}{3}+\frac{2}{3}}=3y^0=3\\\\\text{used:}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\a^\frac{1}{n}=\sqrt[n]{a}\\\\a^{-n}=\dfrac{1}{a^n}\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}\\\\a^0=1,\ a\neq0 [/tex]

The value of the expression after simplification is 3 after applying the property of integer of exponent.

What is integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an expression:

[tex]\rm = \dfrac{(27y^ -^2)^{\dfrac{1}{3}}}{y ^{\dfrac{-2}{3}}}[/tex]

[tex]\rm \rm = \sqrt[3]{27} \ \dfrac{y^{\dfrac{-2}{3}}}{y ^{\dfrac{-2}{3}}}[/tex]

= 3

Thus, the value of the expression after simplification is 3 after applying the property of integer of exponent.

Learn more about the integer exponent here:

brainly.com/question/4533599

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