a student gives ab^3 as an answer when asked to write ab•ab•at using exponents. What is the students error?

Question

please show me/explain to me what the student did wrong

Answer 1

Look at the last item in the equation. It's at not ab. 

 

ab * ab * at = a * a * a * b * b* t = a³b²t

 

If you've made a typo and equation should be ab * ab * ab, the answer would be a³b³ = (ab)³.

 

The parentheses are important, and to illustrate, let's pick some values for a and b.

 

a = 3

b = 5

 

Correct 

a³b³ = 3*5*3*5*3*5 = 15 * 15 * 15 = 3,375

a³b³ = 3*3*3 *5*5*5 = 27 * 125 = 3,375

 

Incorrect 

ab³ = a * b * b * b

ab³ = 3*5*5*5 = 375

 

 

 

 

Answer 2

ababab = aaabbb (by the Commutative Property of Multiplication)

 

           = a³b³ ( or (ab)³ )

 

Note:  ab³ means abbb ( b is cubed, but a is not)

Answer 3

ab*ab*ab=(ab)^3

ab^3 means that only b is cubed; you want both a and b to be cubed

you could also write a³b³

the student forgot the parentheses