Apply the Properties of Integer Exponents to generate equivalent expressions to ◂/▸ 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point) ◂/▸ 2^2/2^−4 =
To generate equivalent expressions with positive exponents, we can use the property that states:
For any non-zero number a and any integers m and n, a^(m/n) = (a^m)^(1/n)
Using this property, we have:
2^2 / 2^-4 = (2^2)^(1/-4)
Now, we can simplify by applying the power rule: (a^m)^n = a^(m*n)
(2^2)^(1/-4) = 2^(2*(-1/-4))
= 2^(2*(1/4))
= 2^(2/4)
= 2^(1/2)
The expression 2^(1/2) represents the square root of 2. So, the solution to the expression is the square root of 2, which is approximately 1.414.
Provide the solution as a whole number
Apologies for the confusion. If we are looking for a solution as a whole number, then we need to simplify the expression further:
2^(1/2) = √2 ≈ 1.414
Therefore, the solution as a whole number is 1.
incorrect
Apologies for the previous incorrect response. Let's continue simplifying the expression:
2^(1/2) can be rewritten as the square root of 2.
The square root of 2 is an irrational number and cannot be represented as a whole number. Therefore, there is no whole number solution for the expression ◂/▸ 2^2/2^−4.