Question

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Annabelle and Navene are multiplying (4^2 7^5)(4^3 7^2).



Annabelle's Work Navene's Work
(4^2 7^5)(4^3 7^2) = 4^2 + ^37^5 + ^2 = 4^5 7^7 (4^2 7^5)(4^3 7^2) = 4^2x^37^5x^2 = 4^6 7^10

Is either of them correct? Explain your reasoning.

Answer 1

Neither of them are correct.

This is what Annabelle is doing:

`(4^2+7^5)(4^3+7^2)`

This is what Navelle is doing:

`(4^27^2)(4^37^2) \implies 4^(2*3)7^(2*5)`

Navelle is multiplying the exponents. You only do that when you raise an exponent to a power under parenthesis. Annabelle mistook multiplication for addition, and she got her answer as a result. This is the correct way to do it:

`4^27^5*4^37^2=4^(2+3)*7^(2+5)=4^5*7^7`