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, we can use the property of integer exponents that says:

a^m ⋅ a^n = a^(m+n)

Applying this property to the given expression 3^7 ⋅ 3^(-9), we get:

3^7 ⋅ 3^-9 = 3^(7+(-9)) = 3^(-2)

Now, to change 3^(-2) to a positive exponent, we can use the property:

a^(-n) = 1/a^n

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

Therefore, the simplified fraction with no remaining exponents is 1/9.

Answer 2

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.

Answer 3

To generate equivalent expressions with only positive exponents, we can use the property of integer exponents that says:

a^m ÷ a^n = a^(m-n)

Applying this property to the given expression 2^2 ÷ 2^-4, we get:

2^2 ÷ 2^-4 = 2^(2-(-4)) = 2^6

Now, the expression is already in positive exponent form. So, to solve the expression:

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

Therefore, the solution as a whole number is 64.