Question

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

Answer 1

Answer:

C

Step-by-step explanation:

The Answer is C on Edge.

Answer 2

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