1 of 5

Question

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.

Answer 1

To generate equivalent expressions with positive exponents, we can use the property of integer exponents that states:
a^m ⋅ a^n = a^(m+n)

Using this property, we can rewrite the expression 3^7⋅3^−9 as:
3^(7+(-9))

Simplifying the exponent, we get:
3^(-2)

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

Applying this property to our expression, we get:
1/3^2

Simplifying further, we get:
1/9

Therefore, the simplified answer is 1/9.