Monique and Allison simplified the same expression but ended up with different answers. Their work is shown below. Monique's work: (2^5)^2*2^(-4)= 2^14. Allison's work: (2^5)^2*2^(-4)= 2^7*2^(-4)=2^3. Did either student simplify the expression correctly? If so tell who and explain how her work follows the laws of exponents. If neither student is correct, simplify the expression and explain how it follows the laws of exponents.

Answer 1

Allison simplified the expression correctly. Her work follows the law of exponents that states when you are multiplying two exponential expressions with the same base, you add the exponents.

In this case, (2^5)^2 * 2^(-4) can be simplified as (2^10) * 2^(-4) = 2^(10-4) = 2^6.

So, the correct simplified expression is 2^3, as found by Allison.