### Answers and Explanations

*x • x = x*^{2}Rewrite*x • x*with exponents.*x*^{1}•*x*^{1}

Bases are the same. Keep the base and add the exponents.*x*^{1}•*x*^{1}=*x*^{1+1}=*x*^{2}-
*x + x =*2**x**

x + x is not the same as x • x. This exercise requires addition of terms, not multiplication.

Add:

x + x = 1x + 1x = 2x *a*^{4}•*b*^{4}=*a*^{4}*b*^{4}

Because the bases are different (a and b), don't add the exponents.*a*^{4}•*b*^{4}=*a*^{4}*b*^{4}^{ }*a*^{-2}•*a*^{6}=*a*^{4}

Bases are the same. Keep the base and add the exponents.*a*^{-2}•*a*^{6}=*a*^{-2+6}=*a*^{4}^{ }**(***xyz*)^{5}• (*xyz*)^{15}= (*xyz*)^{20}

Bases are the same. Keep the base and add the exponents.

(*xyz*)^{5}• (*xyz*)^{15}= (*xyz*)^{5+15}= (*xyz*)^{20}^{ }**(20***e*)(20*e*)= 400*e*^{2}

Rewrite (20*e*)(20*e*) with exponents.

(20*e*^{1})(20*e*^{1})

Bases are the same. Keep the base and add the exponents. (Remember to multiply 20 and 20.)

(20*e*^{1})(20*e*^{1}) = 20***20** e*^{1 }**e*^{1}= 400 **e*^{1+1 }= 400*e*^{2}

**(12 +***y*)^{30}• (12 +*y*)^{8 }= (12 +*y*)^{38}

Bases are the same. Keep the base and add the exponents.

(12 +*y*)^{30}• (12 +*y*)^{8}= (12 +*y*)^{30+8}= (12 +*y*)^{38}^{ }