Question

What expression is equivalent to 7sqrtx^2/5sqrty^3​

Answer 1

Step-by-step explanation:

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7√(x²) 7√(x²)

------------- = ----------------------

5 √(y³) 5√( y^(3/2) )

We want to get the fractional exponent out of the denominator. To do this, multiply both numerator and denominator by y^(1/2):

7√(x²) 7√(x²) y^(1/2) 7√(x²)·y^(1/2) 7x√y

------------- = --------------------- * ----------- = --------------------- = ----------

5 √(y³) 5√( y^(3/2) ) y^(1/2) 5 √(y²) 5y

This is the final answer. We have succeeded in removing radicals / fractional exponents from the denominator.

Answer 2

The expression
`(7√(x^2))/(5√(y^3))` can be simplified to
`(7√(x^2))/(5y√(y))`.

Step-by-step explanation:

Let's simplify the expression
`(7√(x^2))/(5√(y^3))`:

First, simplify the square root terms:

`(7|x|)/(5√(y^3))`

Now, combine the constants:

`(7)/(5) \cdot (|x|)/(√(y^3))`

To simplify further, you can rewrite
`√(y^3)` as
`√(y^2 \cdot y)` and then cancel out one of the y terms:

`(7)/(5) \cdot (|x|)/(y√(y))`

So, the simplified expression is
`(7|x|)/(5y√(y))`, or equivalently,
`(7√(x^2))/(5y√(y))`.