simplify:`xy * x^(7/4) * y^(3/2)` ``

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the expressions:

`xy*(x^(7/4))(y^(3/2))`

We need to simplify.

First we will combine liker terms.

`==gt x*(x^(7/4)) *y*(y^(3/2))`

Now we will use the power properties to simplify.

We know that:

`a^n*a^m = a^(n+m) `

`==gt x*(x^(7/4)) = x^(1+7/4) = x^(11/4) `

`==gt y*(y^(3/2)) = y^(1+3/2) = y^(5/2)`

Then,

`xy*(x^(7/4))*(y^(3/2)) = x^(11/4)* x^(5/2)`

You could also rewrite in radical form:

`==gt x^(11/4)*y^(5/2)= (^4sqrtx)^11 (sqrtx)^5`

mlsiasebs's profile pic

mlsiasebs | College Teacher | (Level 1) Associate Educator

Posted on

Since we have two variables, x and y, in this problem, we need to combine them to simplify the equation.  Remember, that to combine to variables with different powers, we add the powers if we are multiplying them and subtract if we are dividing.  We cannot combine the x and y powers because they are different variables.  We can only combine x terms and y terms.

We can rewrite this to group the x and y terms together.  REarranging does not change the value because all terms are multiplied.

`x*x^(7/4)*y*y^(3/2)`

 Now, we can combine the terms

`x^(1+7/4)*y^(1+3/2)`

and get the following

`x^(11/4)*y^(5/2)`

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