Answer:
16384 or [tex]2^{14}[/tex]
Step-by-step explanation:
This is easiest done by creating identical bases (the number being raised by the exponent, 4 and 8 here).
How do we do that? Well let’s start with [tex]4^{4}[/tex].
For both 8 and 4 the bases can be rooted to 2
[tex]\sqrt[3]{8} = 2 \\ \sqrt{4} = 2[/tex]
Because the root of 4 is 2, that means [tex]2^{2} =4[/tex].
Therefore, we can substitute [tex]2^{2}[/tex] for 4 in [tex]4^{4}[/tex], which looks like this:
[tex]2^{2^{4} }[/tex]
And, we should know that an exponent raised to an exponent is the same as multiplying those exponents together. This means [tex]2^{2^{4}} =2^{8}[/tex].
We can repeat the process with [tex]8^{2}[/tex]
[tex]8 = 2^{3} \\8^{2} =2^{3^{2} } \\2^{3^{2} } =2^{6}\\8^{2}=2^{6}[/tex]
Now that we have [tex]2^{8}\ and\ 2^{6}[/tex] we can continue. Given that the bases are the same we can simply add the exponents together when we multiply.
[tex]2^{8}[/tex] x [tex]2^{6}[/tex] = [tex]2^{14}[/tex] (or 16384).
