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
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents.
First, let's simplify 2^2/2^-4 using the quotient rule for exponents:
2^2/2^-4 = 2^(2 + 4) = 2^6
Now, using the property of a negative exponent: a^(-n) = 1/a^n, we can rewrite 2^6 as:
2^6 = 1/2^-6
Since we want the expression to have only positive exponents, we can further simplify by applying the property of a reciprocal: 1/(1/x) = x.
1/2^-6 = 2^6
Therefore, the equivalent expression with only positive exponents is 2^6.
Now, let's solve 2^6 to find the solution as a whole number:
2^6 = 2 x 2 x 2 x 2 x 2 x 2 = 64
Therefore, the solution to the expression 2^2/2^-4, with equivalent expressions with only positive exponents, is 64.