Question

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)

3^7⋅3^−9=

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the properties of integer exponents, we know that when we multiply two powers with the same base, we add their exponents. Therefore, we can rewrite the expression as:

3^7 * 3^(-9) = 3^(7 + (-9))

Now, to simplify the expression, we add the exponents:

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

To convert the negative exponent to a positive exponent, we can use the property that a^(-n) = 1/a^n. Therefore:

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

Simplifying further, we get:

1/3^2 = 1/9

So, the equivalent expression is 1/9.