Asked by Gelo

Apply the properties of integer exponents to generate equivalent expressions to 3⁷ • 3^‐⁹ with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answers

Answered by GPT 3.5
To apply the properties of integer exponents to generate equivalent expressions, we can use the property that for any positive integer a, a^(-n) = 1/a^n.

So, for the expression 3^7 • 3^(-9), we can rewrite it as 3^7 • 1/3^9.

Now, using the property of exponentiation that a^m • a^n = a^(m+n), we can simplify the expression further:

3^7 • 1/3^9 = 3^(7+(-9)) = 3^(-2) = 1/3^2 = 1/9.

Therefore, the simplified fraction is 1/9.
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