Question

Simplify
^3✓-8x^24 y^36

Answer 1

`\sqrt[3]{-8x^(24)y^(36)} = \sqrt[3]{-8}\cdot \sqrt[3]{x^(24)}\cdot \sqrt[3]{y^(36)}`

`\sqrt[3]{8}=-2` because
`(-2)(-2)(-2)= -8`

`\sqrt[3]{x^(24)}=x^8` because
`(x^8)(x^8)(x^8)=x^(24)`

`\sqrt[3]{y^(36)}=y^(12)` because
`(y^(12))(y^(12))(y^(12))=y^(36)`

Therefore
`\sqrt[3]{-8x^(24)y^(36)} = -2x^8y^(12)`

Answer 2

`-2x^8y^(12)`

Explanation:

Given expression:

`\sqrt[3]{-8x^(24)y^(36)}`

`\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:`

`\implies \sqrt[3]{-8}\sqrt[3]{x^(24)}\sqrt[3]{y^(36)}`

`\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{(1)/(n)}:`

`\implies \left(-8\right)^{(1)/(3)}\left(x^(24)\right)^{(1)/(3)}\left(y^(36)\right)^{(1)/(3)}`

Rewrite 8 as 2³:

`\implies \left(-2^3\right)^{(1)/(3)}\left(x^(24)\right)^{(1)/(3)}\left(y^(36)\right)^{(1)/(3)}`

`\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):`

`\implies -2^{(3)/(3)}x^{(24)/(3)}y^{(36)/(3)}`

Simplify:

`\implies -2x^8y^(12)`