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

Answer 1

To generate an equivalent expression with only positive exponents, we can use the rule that says "a^(-n) = 1/a^n".

So, 3^(-9) can be rewritten as 1/3^9.

Now, we can rewrite the expression 3^7 x 3^(-9) as (3^7) x (1/3^9).

Using the property of multiplication of exponents, we can combine these two terms: 3^7 x 1/3^9 = 3^(7-9).

Simplifying further, 7-9 = -2. Therefore, the expression becomes 3^(-2).

Finally, we can use the rule mentioned earlier to rewrite 3^(-2) as 1/3^2.

Thus, the simplified fraction is 1/3^2.

Therefore, the expression 3^7 x 3^(-9) is equal to 1/3^2, which can be further simplified as 1/9.