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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Mathematics, 22.06.2019 03:30, shygorringe
The length of a rectangular board is 3 feet less than twice its width. a second rectangular board is such that each of its dimensions is the reciprocal of the corresponding dimensions of the first rectangular board. if the perimeter of the second board is one-fifth the perimeter of the first, what is the perimeter of the first rectangular board?
Answers: 3
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Match each expression to its equivalent expression with a rational denominator....
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