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.
To apply the properties of integer exponents, we can rewrite the expression 2^2/2^-4 using the rule a^m/a^n = a^(m-n), where "a" represents the base and "m" and "n" represent the exponents.
So, we have:
2^2 / 2^-4
Using the property mentioned earlier, we can rewrite this expression as:
2^(2 - (-4))
Simplifying further:
2^(2 + 4)
Now, evaluate the expression:
2^6 = 64
Therefore, the solution to the expression 2^2/2^-4, with only positive exponents, is 64.
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.