Question

Simplify the following : x^2y^-3 / x^5y^2​

Answer 1

Answer:

Step-by-step explanation:

$\frac{a^{m}}{a^{n}}=a^{m-n}\\\\a^{-m}=\frac{1}{a^{m}}\\\\\\\frac{x^{2}y^{-3}}{x^{5}y^{2}}=x^{(2-5)}*y^{(-3-2)}\\\\ = x^{-3}*y^{-5}\\\\=\frac{1}{x^{3}y^{5}}$

Answer 2

Remember that exponents (or powers) of the same basis can be divided by subtracting the exponents. For example $\frac{x^n}{x^m} =x^{n-m}$

Using this information, we can easily rearrange our equation to look like this:

$\frac{x^2}{x^5} \frac{y^{-3}}{y^2}$

Now that the basis are the same, we can conveniently subtract the exponents to get the following result:

$x^{-3}y^{-5}$ or $\frac{1}{x^3y^5}$. And that's the final answer.