Compare and Contrast: Below are two expressions. Simplify each and then choose the statement that is true.Expression #1 Expression #2(y9)(2y2)3 (9y)(2y3)2 The exponents in Expression #1 are greater than the exponents of Expression #2. The exponents on Expression #2 are greater than the exponents of Expression #1. The exponents of Expression #1 are the same as the exponents of Expression #2. The relationship cannot be determined with the given information.

Question
Answer:
The answer is the exponents in Expression 1 are greater than the exponents of Expression 2.
Solution:
First, we simplify both expressions. For the power of a product, we can distribute the exponent over the different factors:
     Expression #1: (y^9)(2y^2)^3 => (y^9) [(2^3) (y^2)^3] 
     Expression #2: (9y)(2y^3)^2 => (9y) [(2^2) (y^3)^2] 

When raising exponential to another power, we can multiply the exponents.
     Expression #1: => (y^9) [(2^3) (y^6)]
     Expression #2: => (9y) [(2^2) (y^6)]

We can multiply exponents by taking the sum of the powers.
     Expression #1: => (2^3) (y^15) = 8y^15
     Expression #2: => (3^2) (2^2) (y^7) = 36y^7
Based on our simplified exponents, the Expression #1 exponents are greater than the Expression #2 exponents.
solved
general 11 months ago 2982