Question

Solve for the following exponents(2n³/3n⁴)²

Answer 1

The above expression is simplified as
`((2n^3)/(3n^4) )^2   = (4)/(9n^2)`

Explanation:

Here, the given expression is:

`((2n^3)/(3n^4) )^2`

Laws of Exponents:

1.
`(x^m)/(x^n)    = x^((m-n))`

2.
`((x)/(y) )^k  = (x^k)/(y^k)`

3.
`x^m. x^n  = x^(m +n)`

using the above results, we get:

`((2n^3)/(3n^4) )^2  = ((2n^(3-4))/(3) )^2\\=((2n^((-1)))/(3)) ^2\\=((2)/(3n) )^2  = ((2^2)/((3n)^2) )\\=(4)/(9n^2) \\\implies((2n^3)/(3n^4) )^2   = (4)/(9n^2)`

Hence, the above expression is simplified as
`((2n^3)/(3n^4) )^2   = (4)/(9n^2)`