Find the cube-roots of −27343-\dfrac{27}{343}−34327
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Prime factors of 27:
Prime factors of 343:
−273433=−2733433=−3×3×33(7×7×7)3=−37\sqrt[3]{-\dfrac{27}{343}}\\[1em] = -\dfrac{\sqrt[3]{27}}{\sqrt[3]{343}}\\[1em] = -{\dfrac{\sqrt[3]{3 \times 3 \times 3}}{\sqrt[3]{(7 \times 7 \times 7)}}}\\[1em] = -\dfrac{3}{7}3−34327=−3343327=−3(7×7×7)33×3×3=−73
Hence,−273433=−37\sqrt[3]{-\dfrac{27}{343}} = -\dfrac{3}{7}3−34327=−73
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