Question

How do you simplify `(c^3d^4)/(cd^7)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(c^3/c)(d^4/d^7)`

Next, use these rules of exponents to simplify the `c` terms:

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

`(c^3/c^color(blue)(1))(d^4/d^7) => (c^color(red)(3)/c^color(blue)(1))(d^4/d^7) => c^(color(red)(3)-color(blue)(1))(d^4/d^7) => c^2(d^4/d^7)`

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

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

`c^2(d^color(red)(4)/d^color(blue)(7)) => c^2(1/d^(color(blue)(7)-color(red)(4))) => c^2 * 1/d^3 = c^2/d^3`

Answer 2

`(c^2)/(d^3)`

Explanation:

`"using the "color(blue)"law of exponents"`

`•color(white)(x)a^m/a^n=a^(m-n)to"for "m>n`

`•color(white)(x)a^m/a^n=1/a^(n-m)to" for "n>m`

`(c^3d^4)/(cd^7)`

`=c^3/c^1xxd^4/d^7`

`=c^((3-1))xx1/d^((7-4))`

`=c^2/1xx1/d^3=c^2/d^3`