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