Question

What is the value of ? (2/3)^-4

Answer 1

I hope this helps you



(3/2)^4



3^4/2^4



81/16

Answer 2

Answer: The value is
`5(1)/(16).`

Step-by-step explanation: We are given to find the value of the following exponent:

`E=\left((2)/(3)\right)^(-4).`

We will be using the following properties of exponents:

`(i)~a^(-n)=(1)/(a^n),\\\\(ii)~\left((a)/(b)\right)^n=(a^n)/(b^n).`

We have

`E\\\\\\=\left((2)/(3)\right)^(-4)\\\\\\=\left((3)/(2)\right)^4\\\\\\=(3^4)/(2^4)\\\\\\=(81)/(16)\\\\\\=5(1)/(16).`

Thus, the required value is
`5(1)/(16).`