Mathematics, 10.07.2019 09:00 arichar
(750/512)^1/3 what is equivilant to this? ?
Answers: 1
![\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------](/tpl/images/0072/6693/ad749.png)
![\bf \left( \cfrac{750}{512} \right)^{\frac{1}{3}}\implies \cfrac{750^{\frac{1}{3}}}{512^{\frac{1}{3}}}\implies \cfrac{\sqrt[3]{750^1}}{\sqrt[3]{512^1}}\quad \begin{cases} 750=2\cdot 3\cdot 5\cdot 5\cdot 5\\ \qquad 2\cdot 3\cdot 5^3\\ \qquad 6\cdot 5^3\\ 512=8\cdot 8\cdot 8\\ \qquad 8^3 \end{cases} \\\\\\ \cfrac{\sqrt[3]{750}}{\sqrt[3]{512}}\implies \cfrac{\sqrt[3]{6\cdot 5^3}}{\sqrt[3]{8^3}}\implies \cfrac{5\sqrt[3]{6}}{8}](/tpl/images/0072/6693/15f51.png)
![\frac{5\sqrt[3]{6}}{8}](/tpl/images/0072/6693/ac646.png)
![x^\frac{m}{n}=\sqrt[n]{x^m}](/tpl/images/0072/6693/01ac4.png)
, w ecan write our given number as:![(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{(\frac{750}{512})^1}](/tpl/images/0072/6693/b115d.png)
![(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{750}{512}}](/tpl/images/0072/6693/b8d14.png)
and 750 as 125*6.![(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{125*6}{8^3}}](/tpl/images/0072/6693/64259.png)
![(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{5^3*6}{8^3}}](/tpl/images/0072/6693/6e7a4.png)
![\sqrt[n]{a^n}=a](/tpl/images/0072/6693/b69f6.png)
, we will get:![(\frac{750}{512})^{\frac{1}{3}}=\frac{5\sqrt[3]{6}}{8}](/tpl/images/0072/6693/5fbef.png)
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