Okay, Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7 ⋅ 3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Answer 1

To generate equivalent expressions with only positive exponents using the properties of integer exponents, we can rewrite 3^7 ⋅ 3^−9 as:

3^(7-9) = 3^(-2)

Now, to find the value of 3^(-2), we need to remember that a negative exponent indicates a reciprocal:

3^(-2) = 1/3^2
3^(-2) = 1/9

Therefore, the simplified fraction of 3^7 ⋅ 3^−9 is 1/9.

Answer 2

Same thing with 2^2/2^-4

Answer 3

To generate equivalent expressions with only positive exponents using the properties of integer exponents, we can rewrite 2^2 ÷ 2^(-4) as:

2^2 ÷ 2^(-4) = 2^(2-(-4))
2^2 ÷ 2^(-4) = 2^6

Now, to find the value of 2^6:

2^6 = 64

Therefore, the value of 2^2 ÷ 2^(-4) is 64.