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astra-53 [7]
3 years ago
14

Which expression is equivalent to RootIndex 3 StartRoot 32 x Superscript 8 Baseline y Superscript 10 Baseline EndRoot?

Mathematics
2 answers:
lapo4ka [179]3 years ago
8 0

Answer:

C

Step-by-step explanation:

The Answer is C on Edge.

evablogger [386]3 years ago
5 0

Answer:

The equivalent expression to the given expression is \sqrt[3]{32x^8y^{10}}=2x^2y^3\sqrt[3]{4x^2y}

Step-by-step explanation:

The given expression is \sqrt[3]{32x^8y^{10}}

To find the equivalent expression:

\sqrt[3]{32x^8y^{10}}=(32x^8y^{10})^{\frac{1}{3}}

We may write the above expression as below:

=(32^{\frac{1}{3}})((x^8)^{\frac{1}{3}})((y^{10})^{\frac{1}{3}})

=(2)((4)^{\frac{1}{3}})(x^6)\times (x^2)(x^{\frac{2}{3}})(y^3)(y^{\frac{1}{3}}) (using square root properties)

=(2\sqrt[3]{4})(x^2\sqrt[3]{x^2})(y^3\sqrt[3]{y}) (combining the like terms and doing multiplication )

=2x^2y^3\sqrt[3]{4x^2y}

Therefore \sqrt[3]{32x^8y^{10}}=2x^2y^3\sqrt[3]{4x^2y}

Therefore the equivalent expression to the given expression is \sqrt[3]{32x^8y^{10}}=2x^2y^3\sqrt[3]{4x^2y}

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