Apply the Properties of Integer Exponents to generate equivalent expressions (2 ^ 2)/(2 ^ - 4) with only positive exponents, then solve the expression. Provide the solution as a whole number.
To generate equivalent expressions with only positive exponents, we can use the property of negative exponents which states that for any nonzero base, a, and any integer, n, where n < 0, we have a^n = 1/(a^(-n)).
In this case, we are given (2^2)/(2^(-4)). Applying the property of negative exponents, we can rewrite the expression as (2^2)/(1/(2^4)), which simplifies to (2^2)*(2^4).
Using the property of adding exponents when multiplying with the same base, we can combine 2^2 and 2^4 as 2^(2+4) which gives us 2^6.
Therefore, the expression (2^2)/(2^(-4)) is equivalent to 2^6. Solving 2^6, we get 2*2*2*2*2*2 = 64.
So the solution to the expression (2^2)/(2^(-4)) is 64.
To generate an equivalent expression with only positive exponents, we can use the property of negative exponents, which states that 1/a^b = a^(-b).
Using this property, we can rewrite (2^2)/(2^(-4)) as:
(2^2) * (2^4)
Now, using the property of exponents, which states that a^m * a^n = a^(m + n), we can simplify:
2^(2 + 4)
2^6
Now, we can solve the expression:
2^6 = 2 * 2 * 2 * 2 * 2 * 2
= 64.
So, the solution to the expression (2^2)/(2^(-4)) is 64.