Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)

Question

2^2 over 2−4=

Answer 1

To apply the property of integer exponents, we can use the rule that says when we have a negative exponent, we can rewrite it as its reciprocal with a positive exponent.

Using this rule, we can rewrite 2^(-4) as 1/2^4.

So, the expression becomes:

2^2 / 1/2^4

Next, let's simplify this expression. When we divide by a fraction, it is the same as multiplying by its reciprocal. So, we can rewrite the expression as:

2^2 * 2^4

Now, we can use the property of exponents that says when we multiply two numbers with the same base, we add the exponents. So, 2^2 * 2^4 becomes:

2^(2+4) = 2^6

Finally, calculating 2^6, we get:

2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64

Therefore, the solution to the expression 2^2 / 2^(-4) is 64.