Question

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

Answer 1

Answer:

The above expression is simplified as $(\frac{2n^3}{3n^4} )^2   = \frac{4}{9n^2}$

Step-by-step explanation:

Here, the given expression is:

$(\frac{2n^3}{3n^4} )^2$

Laws of Exponents:

1. $\frac{x^m}{x^n}    = x^{(m-n)}$

2. $(\frac{x}{y} )^k  = \frac{x^k}{y^k}$

3.$x^m. x^n  = x^{m +n}$

using the above results, we get:

$(\frac{2n^3}{3n^4} )^2  = (\frac{2n^{3-4}}{3} )^2\\=(\frac{2n^{(-1)}}{3}) ^2\\=(\frac{2}{3n} )^2  = (\frac{2^2}{(3n)^2} )\\=\frac{4}{9n^2} \\\implies(\frac{2n^3}{3n^4} )^2   = \frac{4}{9n^2}$

Hence, the above expression is simplified as $(\frac{2n^3}{3n^4} )^2   = \frac{4}{9n^2}$