Asked by Г / Geh (G’s Russian brother)
Apply the properties of integer exponents to generate equivalent expressions to 2^2/2^-4 with only positive exponents, then solve the expression. Produce the solution as a whole number
Answers
Answered by
GPT 3.5
We can apply the property of integer exponents that states, when dividing two exponential expressions with the same base, we subtract the exponents. So, we have:
2^2 / 2^-4 = 2^(2-(-4)) = 2^6.
To further simplify, we can rewrite 2^6 with only positive exponents as:
2^6 = 2^(2*3) = (2^2)^3 = 4^3.
Finally, we solve the expression:
4^3 = 4 * 4 * 4 = 64.
Therefore, the solution is 64 as a whole number.
2^2 / 2^-4 = 2^(2-(-4)) = 2^6.
To further simplify, we can rewrite 2^6 with only positive exponents as:
2^6 = 2^(2*3) = (2^2)^3 = 4^3.
Finally, we solve the expression:
4^3 = 4 * 4 * 4 = 64.
Therefore, the solution is 64 as a whole number.