apply the properties of integer exponents to generate equivalent expressions to 2^2/2^-4 with only positive exponents, the solve the expression. provide the solution as a whole number.

Answer 1

To apply the properties of integer exponents and generate equivalent expressions with only positive exponents for 2^(2/2^(-4)), we can use the following rules:

1. The multiplication rule: x^a * x^b = x^(a + b)
2. The division rule: x^a / x^b = x^(a - b)
3. The power of a power rule: (x^a)^b = x^(a * b)
4. The negative exponent rule: x^(-a) = 1 / x^a

First, let's simplify the expression inside the exponent:

2^(-4) = 1 / 2^4 = 1 / 16

Now we can substitute this value back into the original expression:

2^(2/2^(-4)) = 2^(2/1/16)

According to the division rule, dividing by a fraction is the same as multiplying by its reciprocal:

2^(2/1/16) = 2^(2 * 16/1)

Applying the power of a power rule:

2^(2 * 16/1) = 2^(32/1) = 2^32

Therefore, the equivalent expression with only positive exponents is 2^32.

To solve the expression, we can evaluate 2^32:

2^32 = 4294967296

So the solution as a whole number is 4294967296.