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Rzqust [24]
4 years ago
13

Please correct my work and show your work if I MESSED up

Mathematics
1 answer:
sertanlavr [38]4 years ago
4 0

If the first line says

\sqrt[3]{4x^3}\cdot\sqrt[3]{2x^4}

we should first write this as one cube root:

\sqrt[3]{4x^3\cdot2x^4}=\sqrt[3]{8x^7}

Then for any factor under the cube root, we extract any 3rd powers we can. Since 8=2^3 and x^7=x^6\cdot x=(x^2)^3\cdot x, we have

\sqrt[3]{8x^7}=\sqrt[3]{2^3(x^2)^3x}=\sqrt[3]{(2x^2)^3x}=\sqrt[3]{(2x^2)^3}\cdot\sqrt[3]x=2x^2\cdot\sqrt[3]x

Then [1] = 2x^2 and [2] = x.

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