Question

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

Answer 1

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:

$(2/3)^-^4=\frac{1}{(2/3)^4}$

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:

$\frac{1}{(2/3)^4}=\frac{1}{(2^4/3^4)}=\frac{1}{(16/81)}$

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

$\frac{1}{(16/81)}=1\frac{81}{(16)}=\frac{81}{16}$