Question

How do you simplify `(3xy^4)/(9xy)` using only positive exponents?

Answer 1

`y^3/3 " or " 1/3 y^3`

Explanation:

Using the following`color(blue)" rules of exponents "`

`• a^m/a^n = a^(m-n)`

`(3xy^4)/(9xy) = 3/9xx x/x xxy^4/y^1`

`= 1/3 xx 1 xx y^(4-1)= 1/3 y^3`

Answer 2

`y^3/3`

Explanation:

You can separate the numerator and the denominator into three separate terms:
`(3 times x times y^4)/(9 times x times y)`

This will help you to divide the terms that are in like terms (such as 3 and 9, the two x's, and `y^4` and y).

Important Key Concepts To Note:

• remember the quotient rule in exponents.
  `x^b/x^a = x^{b - a}`
• Terms that have no exponents with them, there's always an invisible "1" as the exponent.
  `a = a^1`

Let's separate the terms and divide:
`3/9 times x^1/x^1 times y^4/y^1`
`= 1/3 times 1 times y^3` which is the same thing as `y^3/3`

Answer: `= y^3/3`