Mathematics, 13.07.2019 22:30 cordovatierra16
Match each expression to its equivalent expression with a rational denominator.
Answers: 1
![\dfrac{1}{\sqrt[4]{3x^3y^5}}\cdot\dfrac{\sqrt[4]{3^3xy^3}}{\sqrt[4]{3^3xy^3}}=\dfrac{\sqrt[4]{3^3xy^3}}{\sqrt[4]{3^4x^4y^8}}=\dfrac{\sqrt[4]{3^3xy^3}}{{\sqrt[4]{3^4x^4(y^2)^4}}}=\dfrac{\sqrt[4]{3^3xy^3}}{3xy^2}](/tpl/images/0086/4006/c9a90.png)
![\dfrac{3}{\sqrt[4]{27x^{11}y^{13}}}=\dfrac{3}{\sqrt[4]{3^3x^{11}y^{13}}}=\dfrac{3}{\sqrt[4]{27x^{11}y^{13}}}\cdot\dfrac{\sqrt[4]{3xy^3}}{\sqrt[4]{3xy^3}}=\dfrac{3\sqrt[4]{3xy^3}}{\sqrt[4]{3^4x^{12}y^{16}}}\\\\=\dfrac{3\sqrt[4]{3xy^3}}{\sqrt[4]{3^4(x^3)^4(y^4)^4}}=\dfrac{3\sqrt[4]{3xy^3}}{3x^3y^4}=\dfrac{\sqrt[4]{3xy^3}}{x^3y^4}](/tpl/images/0086/4006/1957a.png)
![\dfrac{2}{\sqrt[6]{2x^7y^5}}=\dfrac{2}{\sqrt[6]{2x^7y^5}}\cdot\dfrac{\sqrt[6]{2^5x^5y}}{\sqrt[6]{2^5x^5y}}=\dfrac{2\sqrt[6]{2^5x^5y}}{\sqrt[6]{2^6x^{12}y^6}}=\dfrac{2\sqrt[6]{2^5x^5y}}{\sqrt[6]{2^6(x^2)^6y^6}}\\\\=\dfrac{2\sqrt[6]{2^5x^5y}}{2x^2y}=\dfrac{\sqrt[6]{32x^5y}}{x^2y}](/tpl/images/0086/4006/58f49.png)
![\dfrac{4}{\sqrt[6]{32x^5y^9}}=\dfrac{4}{\sqrt[6]{2^5x^5y^9}}\cdot\dfrac{\sqrt[6]{2xy^3}}{\sqrt[6]{2xy^3}}=\dfrac{4\sqrt[6]{2xy^3}}{\sqrt[6]{2^6x^6y^{12}}}=\dfrac{4\sqrt[6]{2xy^3}}{\sqrt[6]{2^6x^6(y^2)^6}}\\\\=\dfrac{4\sqrt[6]{2xy^3}}{2xy^2}=\dfrac{2\sqrt[6]{2xy^3}}{xy^2}}](/tpl/images/0086/4006/46bb1.png)
![\text{Used:}\\\\\sqrt[n]{a^n}=a\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}\\\\\sqrt[n]{a\cdot b}=\sqrt[n]a\cdot\sqrt[n]b](/tpl/images/0086/4006/d7f25.png)
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Match each expression to its equivalent expression with a rational denominator....
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