Question

a friend is having trouble with exponents and asks you to review some worked probelems look over the problems and correct any mistakes find the correct answer and explain the error in the student's reasoning

Answer 1

We have the following expression:

$2x^2y\cdot3x^5y^2$

By combining similar terms, we get

$2\cdot3\cdot x^2\cdot x^5\cdot y\cdot y^2$

now, 2 times 3 is 6 and to add exponents, both the exponents and variables should be alike:

$x^2\cdot x^5=x^{2+5}=x^7$

Similarly,

$y\cdot y^2=y^{1+2}=y^3$

Therefore, the answer is

$6x^7y^3$