Question

a. Is the expression a12•a4 equivalent to a8•a8? Explain.

Answer 1

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:

$x^3*y^2=x^3y^2$  (can't combine because they have different bases of x and y)

$x^3*x^5=x^{(3+5)}=x^8$

$5^2*5^1=5^{(2+1)}=5^3=125$

$a^{12}*a^4=a^{(12+4)}=a^{16}$

$a^8*a^8=a^{(8+8)}=a^{16}$  

The expressions are equivalent because they both simplify and are equal to a^16