Find the cube-roots of −27125-\dfrac{27}{125}−12527
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Prime factors of 27:
Prime factors of 125:
−271253=−2731253=−(3×3×3)3(5×5×5)3=−35\sqrt[3]{-\dfrac{27}{125}}\\[1em] = {-\dfrac{\sqrt[3]{27}}{\sqrt[3]{125}}}\\[1em] = {-\dfrac{\sqrt[3]{(3 \times 3 \times 3)}}{\sqrt[3]{(5 \times 5 \times 5)}}}\\[1em] = -{\dfrac{3}{5}}3−12527=−3125327=−3(5×5×5)3(3×3×3)=−53
Hence, −271253=−35\sqrt[3]{-\dfrac{27}{125}} = {-\dfrac{3}{5}}3−12527=−53
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