Respuesta :
Answer: The value is [tex]5\dfrac{1}{16}.[/tex]
Step-by-step explanation: We are given to find the value of the following exponent:
[tex]E=\left(\dfrac{2}{3}\right)^{-4}.[/tex]
We will be using the following properties of exponents:
[tex](i)~a^{-n}=\dfrac{1}{a^n},\\\\(ii)~\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}.[/tex]
We have
[tex]E\\\\\\=\left(\dfrac{2}{3}\right)^{-4}\\\\\\=\left(\dfrac{3}{2}\right)^4\\\\\\=\dfrac{3^4}{2^4}\\\\\\=\dfrac{81}{16}\\\\\\=5\dfrac{1}{16}.[/tex]
Thus, the required value is [tex]5\dfrac{1}{16}.[/tex]
