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.
3^7 x 3^-9 = ?
To generate an equivalent expression with only positive exponents, we use the property of exponents that states "when you multiply two powers with the same base, you add the exponents."
So in this case, we have 3^7 x 3^-9. Using the property mentioned above, we can add the exponents:
3^7 x 3^-9 = 3^(7 + (-9))
Now we simplify the exponent by adding:
3^(-2)
To solve this expression, we use the property of exponents that states "a negative exponent is equal to the reciprocal of the positive exponent."
So we rewrite 3^(-2) as 1/3^2:
3^(-2) = 1/3^2
Simplifying 1/3^2 gives us:
1/9
Therefore, 3^7 x 3^-9 can be simplified to 1/9.