Question

Which expression is equivalent to

128xy
5 ? Assume x > 0 and y> 0.
2xy5
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Answer 1

The expression equivalent to
`\((128xy)/(5)\) is \(8xy\).`

Step-by-step explanation:

To simplify the given expression,
`\((128xy)/(5)\)`, we divide both the numerator and the denominator by their greatest common factor, which is 5. This simplification yields
`\((128)/(5) * xy\)`. Further simplifying
`\((128)/(5)\)` results in 8, giving us the equivalent expression
`\(8xy\).`

Breaking down the steps, we start with
`\((128xy)/(5)\)`. Dividing both 128 and 5 by 5 simplifies the fraction to
`\((128)/(5)\)`. When multiplied by
`\(xy\),` we obtain the simplified expression
`\(8xy\)`. Therefore,
`\(8xy\)` is the equivalent expression to
`\((128xy)/(5)\).`

In summary, the process involves dividing by the greatest common factor to simplify the fraction and arrive at the equivalent expression
`\(8xy\).`

Complete the question:

Which expression is equivalent to
`\((128xy)/(5)\)`? Assume
`\(x > 0\)` and
`\(y > 0\).`

Answer 2

`√(128x^8y^3) = 8 x^4 y √(2y)`

Step-by-step explanation:

Given

`√(128x^8y^3)` --- the complete expression

Required

The equivalent expression

We have:

`√(128x^8y^3)`

Expand

`√(128x^8y^3) = √(128* x^8 * y^3)`

Further expand

`√(128x^8y^3) = √(64 * 2* x^8 * y^2 * y)`

Rewrite as:

`√(128x^8y^3) = √(64 * x^8 * y^2* 2 * y)`

Split

`√(128x^8y^3) = √(64 * x^8 * y^2) * √(2 * y)`

Express as:

`√(128x^8y^3) = (64 * x^8 * y^2)^(1)/(2) * √(2y)`

Remove bracket

`√(128x^8y^3) = (64)^(1)/(2) * (x^8)^(1)/(2) * (y^2)^(1)/(2) * √(2y)`

`√(128x^8y^3) = 8 * x^(8)/(2) * y^(2)/(2) * √(2y)`

`√(128x^8y^3) = 8 * x^4 * y * √(2y)`

`√(128x^8y^3) = 8 x^4 y √(2y)`