Question

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

Answer 1

Answer: 81/16

Explanation:

When you have a negative exponent, it is equivelant to taking the reciprocal of the exponential and making the exponent positive:

`(2/3)^-^4=(1)/((2/3)^4)`

Distribute the exponent to the base. We are able to do this because the base is composed of a single term. If it were composed of addition and subtraction, you cannot distribute the exponent:

`(1)/((2/3)^4)=(1)/((2^4/3^4))=(1)/((16/81))`

Dividng by a fraction is equivalent to multiplying by the reciprocal:

`(1)/((16/81))=1(81)/((16))=(81)/(16)`