Answer: 81/16
Step-by-step explanation:
When you have a negative exponent, it is equivelant to taking the reciprocal of the exponential and making the exponent positive:
[tex](2/3)^-^4=\frac{1}{(2/3)^4}[/tex]
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:
[tex]\frac{1}{(2/3)^4}=\frac{1}{(2^4/3^4)}=\frac{1}{(16/81)}[/tex]
Dividng by a fraction is equivalent to multiplying by the reciprocal:
[tex]\frac{1}{(16/81)}=1\frac{81}{(16)}=\frac{81}{16}[/tex]
