Respuesta :
Option D: [tex]\frac{81}{16}[/tex] is the value of [tex]\left(\frac{2}{3}\right)^{-4}[/tex]
Explanation:
The given expression is [tex]\left(\frac{2}{3}\right)^{-4}[/tex]
We need to determine the value of the given expression.
To determine the value, let us simplify the expression.
Applying the exponent rule in the expression [tex]a^{-b}=\frac{1}{a^{b}}[/tex], we have,
[tex]\frac{1}{\left(\frac{2}{3}\right)^{4}}[/tex]
Let us apply the exponent rule that [tex]\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}[/tex] , we get,
[tex]\frac{1}{(\frac{2^{4}}{3^{4}})}[/tex]
Simplifying, we get,
[tex]\frac{1}{(\frac{16}{81})}[/tex]
Let us apply the fraction rule that [tex]\frac{1}{c}=\frac{c}{b}[/tex] , we have,
[tex]\frac{81}{16}[/tex]
Thus, the value of the expression [tex]\left(\frac{2}{3}\right)^{-4}[/tex] is [tex]\frac{81}{16}[/tex]
Hence, Option D is the correct answer.
