Monique and Allison simplified the same expression, but ended up with different answers. The work is shown below.
monique:
(2^5)^5 x 2^(-4) = 2^10 x 2^(-4)
allison:
(2^5)^2 x 2^(-4)=2^7x2^(-4)
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, simplified the expression, and explain how it follows the laws of exponents.
Monique simplified the expression correctly.
Monique's work follows the laws of exponents because when raising a power to another power, you multiply the exponents. So (2^5)^5 simplifies to 2^(5*5) which equals 2^25. Then when you multiply 2^25 by 2^(-4), you add the exponents (25 + (-4)) to get 2^21.
Allison's work is incorrect because when raising a power to a power, you must multiply the exponents, not the bases. So (2^5)^2 should simplify to 2^(5*2) which is 2^10, not 2^7 as Allison calculated.