When you multiply a base with an exponent by a base with an exponent, you add the exponents together. (But you can only combine the exponents when the bases are the same)
For example:
[tex]x^3*y^2=x^3y^2[/tex] (can't combine because they have different bases of x and y)
[tex]x^3*x^5=x^{(3+5)}=x^8[/tex]
[tex]5^2*5^1=5^{(2+1)}=5^3=125[/tex]
[tex]a^{12}*a^4=a^{(12+4)}=a^{16}[/tex]
[tex]a^8*a^8=a^{(8+8)}=a^{16}[/tex]
The expressions are equivalent because they both simplify and are equal to a^16
