Question

How do you simplify `\frac { 56x ^ { 4} y ^ { 3} } { 8x y ^ { 7} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`56/8(x^4/x)(y^3/y^7) => 7(x^4/x)(y^3/y^7)`

Next, uses these rules of exponents to simplify the `x` terms:

`a = a^color(blue)(1)` and `x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`7(x^color(red)(4)/x^color(blue)(1))(y^3/y^7) => 7x^(color(red)(4)-color(blue)(1))(y^3/y^7) => 7x^3(y^3/y^7)`

Now, use this rule of exponents to simplify the `y` terms:

`x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`7x^3(y^color(red)(3)/y^color(blue)(7)) => 7x^3(1/y^(color(blue)(7)-color(red)(3))) => 7x^3(1/y^4) =>`

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

Answer 2

`(56x^4y^3)/(8xy^7)=(7x^3)/y^4`

Explanation:

It is easier to understand the simplification of this expression by simplifying the terms individually:

Then: `56/8=7to` is normal division

`x^4/x=x^3to` division of exponents means subtract bottom from top

`y^3/y^7=1/y^4to` division of exponents again means subtract, b from t

And a negative exponent value means you are dividing it into `1`.

Re-assembling the expression: `(56x^4y^3)/(8xy^7)=(7x^3)/y^4`