(40 points) Which expression is equivalent to 3^2 ⋅ 3^−5? (not giving answer choices for the best result)
Mathematics · Middle School · Sun Jan 24 2021
Answered on
Given the equation:
(3^2)(3^-5)
Determine the equivalent expression.
Solution:
In order to solve the equation, we must simply apply the rules of exponent, which deals with multiplying numbers of the same base. This can be represented by,
(n^a)(n^b)
= n^(a + b)
This means that when we multiply numbers of the same base, we simply need to add the base of those numbers.
= (3^2)(3^-5)
= (3)^(2 + (-5))
= (3)^(2 - 5)
= (3)^(-3)
= 1 / 3^3
= 0.037
Final answer:
= 0.037