Question

please answer. I hope you can answer this. Please simplify it .​

Answer 1

Solution!!

$\sf \to \dfrac{\left(\dfrac{-5}{9}\right)^{4}}{\left(\dfrac{-5}{9}\right)^{12}\times \left(\dfrac{-5}{9}\right)^{8}}$

Calculate the product by applying the product rule of exponents.

Product rule of exponents → $\sf a^{m}\times a^{n}=a^{m+n}$

$\sf \to \dfrac{\left(\dfrac{-5}{9}\right)^{4}}{\left(\dfrac{-5}{9}\right)^{12+8}}$

$\sf \to \dfrac{\left(\dfrac{-5}{9}\right)^{4}}{\left(\dfrac{-5}{9}\right)^{20}}$

Using the quotient rule of exponents.

Quotient rule of exponents → $\sf \dfrac{a^{m}}{a^{n}}=a^{m-n}$

$\sf \to \left(\dfrac{-5}{9}\right)^{4-20}$

$\sf \to \left(\dfrac{-5}{9}\right)^{-16}$

$\sf \to \left(\dfrac{9}{-5}\right)^{16}$

$\sf \to \dfrac{9^{16}}{-5^{16}}$

FYI, the product rule and quotient rule of exponents can only be applied if the base is same.