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Juli2301 [7.4K]
3 years ago
6

Which expression is equivalent??? help!

Mathematics
1 answer:
dexar [7]3 years ago
5 0

Answer:

The equivalent expression for the given expression \sqrt[3]{256x^{10}y^{7} } is

4x^{3} y^{2}(\sqrt[3]{4xy} )

Step-by-step explanation:

Given:

\sqrt[3]{256x^{10}y^{7} }

Solution:

We will see first what is Cube rooting.

\sqrt[3]{x^{3}} = x

Law of Indices

(x^{a})^{b}=x^{a\times b}\\and\\x^{a}x^{b} = x^{a+b}

Now, applying above property we get

\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y   )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})

∴ The equivalent expression for the given expression \sqrt[3]{256x^{10}y^{7} } is

4x^{3} y^{2}(\sqrt[3]{4xy} )

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