Question

Nicholas says that (2^6)(2^6) equals 2^12, which also equals 4^6. is this true? PLEASE EXPLAIN

Answer 1

$a^b \cdot a^c= a^{b+c}\\ a^c \cdot b^c=(ab)^c\\\\ 2^6 \cdot 2^6 =2^{6+6}=\underline{2^{12}}=(2\cdot2)^6=\underline{4^6}$

So, yes, it's true.

Answer 2

When you multiply two numbers in exponential notation whose bases are the same, you just keep the base the same and add the exponents.

In this case, you have (2^6) * (2^6) = 2^(6 + 6) = 2^12.

We can change the base of 4^6 into 2:

(2^2)^6

Is this the same as 2^12? Well, when we have an expression like that above, we multiply the exponents together, so we get: (2^2)^6 = 2^12.

Therefore, Nicholas is correct.